Anatolii Platonovich Prudnikov

Obituary

The outstanding Russian mathematician Anatolii Platonovich Prudnikov passed away on January 10, 1999, four days before the age 72.

Prudnikov was born in Ul'janovsk on January 14, 1927. In 1930 the Prudnikov's family moved to Samara. He graduated from high school there in 1944 and the same year he entered Kuibyshev Aviation Institute. In 1947, having nished three grades at this Institute, he became a forth-year student of the Department of Mathematics and Mechanics at Kuibyshev Pedagogical Institute.

Prudnikov graduated from this Institute in 1949 and after that his professional experience started from teaching mathematics in high school and afterwards, a position of Assistent of Professor at Kuibyshev Industrial Institute. In 1952 he was admitted as a post-graduate to this Institute. On February of 1954 Prudnikov was directed to nish his post-graduate course to the Institute of Precise Mechanics and Computing Technique of the Academy of Sciences of the USSR under the supervisorship of Professor Ditkin. On March of 1954 he started to work at this Institute as a Junior Researcher simultaneously with studying as a post graduate. He occupied this position after finishing his post-graduate course. In 1955 he continues this job at the Computer Center of Academy of Sciences of the USSR just then organized. There he worked for more than 43 years, starting from Junior Researcher and becoming the head of the Department. Prudnikov defended his Ph.D. dissertation “Analytic investigations of processes in heat and mass exchanges” in 1957, and his D.Sc. dissertation “On a class of integral transforms of Volterra type and some generalizations of operational calculus” in 1968. In 1972 he was awarded Professor's title, this as an ocial title being always considered as a title of a very high level in the USSR.

The first area of Prudnikov's mathematical research was operational calculus. His interests in this field, closely connected with applied mathematics, were formed under the influence of Professor Ditkin. They were based on both the development of theoretical methods and applications to solution of some special problems of importance in science and practice. The result of their close cooperation was their first book [8] published in 1958 and devoted to operational calculus with respect to two variables. Anatolii Platonovich gave an essential contribution to the justification and development of the operational method suggested by Heaviside. Within the framework of the classical problems of operational calculus he constructed the theory of certain classes of differential and difference operators, including generalized Bessel operators, which essentially extended the set of problems solved by the operational method. He applied the method of operational calculus, developed by him, to solve a series of problems in the theory of heat conductivity and thermodiffusion. These investigations were reflected in the books [13] and [23] and in the handbook [24], and they were highly estimated by specialists. In particular, Professor Prudnikov together with Professor Ditkin and Professor Maslov (at present the academician of Russian Academy of Sciences) were awarded by the State Prize of the USSR in 1975.

The second area of Prudnikov's mathematical research was connected with integral transforms and special functions. He began to work in the field of integral transforms together with V.A.Ditkin [13] and continued this with his student Yu.A.Brychkov. Their results in the theory of integral transforms of generalized functions were presented in the book [48]. This was the first monograph in which a survey of properties of various integral transforms in spaces of test and generalized functions was given. Such a survey of the results in the theory of multidimensional integral transforms was presented in the book [92] written together with Brychkov, Glaeske and Vu Kim Tuan. This was also the first monograph devoted to the theory of multi-dimensional integral transforms. Recently, Prudnikov and Moiseev obtained interesting results on generalized Fourier sine- and cosine-transforms and related orthogonal systems of special functions and orthogonal polynomials. Prudnikov`s interest to special functions began from the joint work with Berlyand and Gavrilova on tables of integral error functions and Hermite polynomials [12]. Later he was an initiator of creating five books [56], [62], [71], [90], [91] and a table of indefinite integrals [66] written together with Brychkov and Marichev. These fundamental handbooks, devoted to the evaluation of integrals and series and direct and inverse Laplace transforms of elementary and special functions, considerably cover all known results. Unlike other similar handbooks they contain many new formulas and integrals of general form which can be applied to evaluate wide classes of new integrals. Moreover, they contain properties of many special functions which were not mentioned earlier in monographic literature. These handbooks are very useful not only to mathematicians, but also to specialists in physics, mechanics, chemistry, engineering, etc who apply methods of mathematical analysis. Anatolii Platonovich worked very actively till his last days. In December of 1998 he together with Kilbas and Marichev finished a new handbook [101], which may be considered as a continuation of the above. It is devoted to evaluation of Mellin transfroms of elementary and special functions.

The third area of Prudnikov's mathematical research was concentrated in informatics. His interests included a wide spectrum of problems in mathematical modelling, algorithmic approach and numerical analysis in connection with applications in computing technique. He developed analytic and numerical methods for solving boundary value problems for the Laplace equation in special domains which arise in such physical problems as optimization of profiles of rolling of rotating vibrations, a torsion of prismatic rods with complicated profile of transverse section, etc. In 1992-1996 he developed problems of mathematical modelling and numerical investigations connected with the control of aerodynamic characteristics of apparatus. Last years Prudnikov was a chief of the investigations in medical informatics in the State Research Experimental Institute of Aviation and Cosmic Medicine. Under his guidance the complex of mathematical models, algorithms, programs and nomograms was created which was aimed to medical investigations on estimation of a professional health of pilots and a level of radiation and electromagnetic pollution of environments.

The results of Prudnikov's scientific activity have been published in more than 100 articles including 10 monographs translated in England, France, Germany, Japan, Poland and USA. Theoretical results obtained in his books and papers are directed to the solution of problems in various fields of science and practice. His books became a table handbooks for researches and engineers.

From the very beginning of his start at Kuibyshev Industrial Institute, Anatolii Platonovich paid a lot of attention to mathematical education, devoted much strength and energy to the supervision of postgraduates and trainees, conducting seminars in the Computer Center and giving simultaneously lectures in the All-Union Institute of Food Industry. He created a group of mathematicians who developed investigations on applications of computing technique to the problems of applied mathematics and informatics. 15 of his students defended PhD thesis under his supervisorship and two of them defended higher dissertations of Doctors of Sciences.

Prudnikov was well known in Russia and other countries of the former USSR as well as abroad. Below we cite the phrase from the paper “Anatolii Platonovich Prudnikov (on the occasion of his seventieth birthday) (Russian)” published in Differentsal'nye Uravnenija 33 (1997), no. 6, 730-736, and written by Russian academicians S.V. Emel'yanov, Yu.I. Zhuravlev, V.A. Il'in, O.A.Oleinik, Ju.V. Prohorov and A.A. Samarskii and corresponding member E.I. Moiseev: “At present he is the main specialist in Russia in the field of operational calculus, integral transforms and special functions”. He was invited to give reports as an invited lecturer at many International Conferences, Seminars and Workshops in former USSR as well as in Bulgaria, Germany, Great Britain, Japan, Spain and Jugoslavia. He was Invited Professor in Fukuoka (Japan), Jena (Germany) and Valencia (Spain). He actively took part in the organization of many USSR or international conferences as a member of Organizing Committee. In particular, he was a Vice-director of International Conference on Generalized Functions and their Applications in Mathematical Physics held in Moscow in 1980.

Prudnikov gave a lot of his energy to publishing activity. For a long time he was a member of the Editorial Board of the All-Union journal Inzhenerno-Fizicheskii Zhurnal translated in English, a member of the Publishing Council in the Ministry of Education of the USSR, Chief of Publishing Council of Computer Center and Editor-in-Chief of all their Proceedings. He was well known as a good organizer and a person producing a positive impression on any partner in negotiations.

Last years Prudnikov was busy with a lot of Editor's work under the “Gordon & Breach Science Publishers”. He was the organizer of the International journal Integral Transfroms and Special Functions which started in 1993, and was an active Editor-of-Chief of this journal, devoting much time to his duties in this journal till the last days. Professor Prudnikov paid a lot of attention to the monograph series “Analytical Methods and Special Functions” published by “Gordon & Breach Science Publishers”, of which he was also the Editor-in-Chief. He was also engaged into the activity connected with the Information Bulletin Integral Transforms and Special Functions (in Russian) prepared by the research group of the journal Integral Transforms and Special Functions and published by the Computer Center of the Russian Academy of Sciences.

Prudnikov took a very active part in public and scientific life in Russia (in the USSR before) and abroad. He was a Scientific Secretary of Computer Center and a Chief of the post-graduate courses there, a member of Director Body of scientifical and methodological Council in mathematics, physics and astronomy of Russian society "Znanie", a member and Vice-Chief of Expert Council in the Supreme Attestation Commission of the USSR and later Russia in mathematics and mechanics. Last years he was a Chief of such an Expert Council in the Supreme Attestation Commission of Russia and a member of Dissertation Councils of Experts in Computer Center and in Moscow State University. He was a member of London and American Mathematical Societies.

Prudnikov had a bright and original personality, was a joyful and witty person, and was very benevolent, tolerant and communicable. Many of those who got to know Anatolii Platonovuich honestly believed (and were, in a way, right) that it was with them that he had his most confidential relations. He had an interest to many parts of human life including music, sport, politics and especially books, but the main thing in his life was communication with people, and everyone who ever met him found a sincere interest in talking with him.

Prudnikov will be remembered for his contribution to Operational Calculus, Integral Transfroms and Special Functions, his genuine manner, limitless energy and enthusiasm. He is survived by his wife Dagma Germanovna and a son Aleksandr Prudnikov, an applied mathematician.

There are some people, who, because of their innate ability and knowledge, their kindness and their willingness to help others, make life much more pleasant for their friends and colleagues. Prudnikov was one of them.

Bright memories of Anatolii Platonovich Prudnikov will forever remain in our heart.

Stafan G. Samko, University of Algarve, Portugal
Evgenii I. Moiseev, Moscow State University, Russia
Hans-Jurgen Glaeske, Jena University, Germany
Anatoly A. Kilbas, Belarusian State University, Belarus
Megumi Saigo, Fukuoka University, Japan

Published in Integral Transforms and Special Functions 6 (1999), No. 1-2, 1-2.

Publications of A. P. Prudnikov

[1] A solution of a mixed problem in the integral form for a system of two parabolic differential equations (Russian). Dokl. Akad. Nauk SSSR (N.S.) 115 (1957), no. 5, 869-871. (Reviews in Mathematical Reviews MR 20 #1848; Zentralblatt fuer Mathematic Zbl.81,92).

[2] A solution of some problems in the theory of molecular transfer for solids of the simplest geometric form (Russian). Izv. AN SSSR. Otd. Tehn. Nauk 1957, No 8, 143-145.

[3] The solution of a mixed boundary problem in the thermodiffusion theory (Russian). Dokl. Akad. Nauk SSSR 119 (1958), no. 2, 249-251. (MR 20 #5359; Zbl.83,91).

[4] To an investigation of heat and mass transfer in dispersion surroundings (Russian). Inzh.-Fiz. Zh. 1 (1958), no. 4, 81-86.

[5] Analytic investigation of processes of heat and mass transfer in convective drying (Russian). Izv. Akad. Nauk SSSR. Otd. Tehn. Nauk 1958, No. 10, 63-67. (MR 20 #7512; Zbl.112,416).

[6] To an investigation of phenomena of transfer of the heat and substance in heavy surroundings (Russian). Dokl. AN BSSR. 2 (1958), no. 8, 334-337 (with A.V. Lykov).

[7] To an investigation of processes of heat and mass transfer while heating and drying a fuel in energotechnological installations (Russian). Izv. AN BSSR. Ser. Fiz.-Tehn. Nauk, 1958, No. 3, 11-23.

[8] Operational Calculus in Two Variables and its Applications (Russian). Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1958, 178 pp (with V.A. Ditkin). (MR 22 #881; Zbl.126,314).

[9] To the theory of ltration of in the graunds (Russian). Izv. AN SSSR. Energetika i Avtomatika, 1959, No. 1, 119-121.

[10] On a problem in the theory of heat conduction (Russian). Inzh.-Fiz. Zh. 3 (1960), no. 5, 136-137.

[11] Functions satisfying the differential equation y''+-2xy'+- 2xy = 0 (Russian). Inzh.-Fiz. Zh. 3 (1960), no. 9, 103-107 (with O.S. Berlyand and R.I. Gavrilova). (MR 23 #A2566).

[12] Tables of integral error functions and Hermite polynomials (Russian). Izd. AN BSSR, Minsk, 1961, 164 pp (with O.S. Berlyand and R.I. Gavrilova).

[13] Integral Transfroms and Operational Calculus (Russian). Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1961, 524 pp (with V.A. Ditkin). (Zbl.99,89).

[14] On the theory of operational calculus (Russian). Dokl. Akad. Nauk SSSR 142 (1962), no. 4, 794-797; English transl. in Soviet Math., Doklady 3 (1962), 172-176. (MR 24 #A3481; Zbl.118,316).

[15] On functions satisfying the differential equation x^2y''' +3xy''+y' +x^2y = 0 (Russian). Dokl. Akad. Nauk SSSR 144 (1962), no. 1, 56-57; English transl. in Soviet Math., Doklady 3 (1962), 672-674. (MR 25 #2257; Zbl.127,294).

[16] Operational calculus of Bessel operators (Russian). Z. Vychisl. Mat. i Mat. Fiz. 2 (1962), no. 6, 997-1018 (with V.A. Ditkin); English transl. in USSR Comput. Math. Math. Phys. (1964), 1184-1212. (MR 26 #6704; Zbl.141,114).

[17] Operational Calculus in Two Variables and its Applications. International Series of Monographs on Pure and Applied Mathematics, Vol. 24. Pergamon Press, New York-Oxford-London-Paris, 1962, 167pp (with V.A. Ditkin). (MR 25 #2397; Zbl.116,309).

[18] Tables of integral error functions and Hermite polynomials. A Pergamon Press book, The Macmillan Co., New York, 1962, 163 pp (with O.S. Berlyand and R.I. Gavrilova). (MR 27 #5937; Zbl.105,113).

[19] On the theory of operational calculus stemming from the Bessel equation (Russian). Z. Vychisl. Mat. i Mat. Fiz. 2 (1963), no. 3, 223-238 (with V.A. Ditkin); English transl. in USSR Comput. Math. Math. Phys. 3 (1963), 296-315. (MR 27 #2817; Zbl.142,396).

[20] On operational calculus of functions of integer argument and some of their aplications in discrete analysis (Russian). Inzh.-Fiz. Zh. 7 (1964), no. 7, 101-115 (with V.A. Ditkin).(Zbl.141,115).

[21] Integral Transforms and Operational Calculus (Polish). PWN, Warszawa, 1964, 343 pp (with V.A. Ditkin).

[22] Integral Transforms and Operational Calculus. Pergamon Press, Oxford-Edinburgh-New York, 1965, 529 pp (with V.A. Ditkin). (MR 33 #4609; Zbl.133,62).

[23] Handbook on Operational Calculus (Russian). Vysshaja Shkola, Moscow, 1965, 466 pp (with V.A. Ditkin). (Zbl.126,314).

[24] Operational Calculus (Russian). Vysshaja Shkola, Moscow, 1966, 404 pp (with V.A. Ditkin). (Zbl.148,367).

[25] Operational calculus. (Russian) Mathematical Analysis, 1964 (Russian), pp. 7-75; Akad. Nauk SSSR Inst. Nauchn. Informacii, Moscow, 1966 (with V.A. Ditkin). (MR 33 #4610).

[26] Operational calculus of functions of two integral variables and its aplications in discrete analysis (Russian). Vierter Internationaler Kongres ueber Anwendungen der Mathematik in den Ingenierurwissenschaften mit dem Rahmenthema: Anwendungen elektronisher Rechenanlagen in Bauwesen (Weimar, 1967), Berichte, Band. 2. Section 2: Angewande Mathematik, 1967, 158-159.

[27] Formulaire pour le calcul op erationnel (French). Masson e Cie, editurs, Paris, 1967, 468 pp (with V.A. Ditkin). (MR 36 #1931; Zbl.146,362).

[28] A method for introducing the finite parts of divergent integrals, and applications of them in operational calculus (Russian). Differentsial'nye Uravnenija 3 (1967), no. 10, 1772-1781 (with V.A. Ditkin) (MR 36 #4282; Zbl.155,450); English transl. in Differenial Equations 3 (1967), 922-926. (Zbl.233.44006).

[29] Integral transfroms (Russian). Mathematical Analysis, 1966 (Russian), pp. 7-82; Akad. Nauk SSSR Inst. Nauchn. Informacii, Moscow, 1967 (with V.A. Ditkin); English transl. in Progress Math. 4 (1969), 1-85. (MR 58 #2037; Zbl.197,379).

[30] On bilinear expansions containing Legendre polynomials (Russian). Dokl. AN BSSR. 12 (1968), no. 2, 119-122. (Zbl.203,62).

[31] Existence of singular points for functions representable by a Laplace integral (Russian). Dokl. Akad. Nauk BSSR 12 (1968), no. 3, 230-234. (MR 37 #1899; Zbl.159,413).

[32] Operational Calculus. Progress in Mathematics 1 (1968), Plenum Press, New York, 1-74 (with V.A. Ditkin).

[33] Integral Transforms. Progress in Mathematics, 4 (1969), Plenum Press, New York, 1-85 (with V.A. Ditkin). (Zbl.197,379)

[34] To the theory of operational calculus (Russian). Dokl. AN BSSR. 13 (1969), no. 3, 222-224. (Zbl.179,201).

[35] Operational calculus of functions of two intgral arguments and some of their applications (Russian). Inzh.-Fiz. Zh. 17 (1967), no. 4, 697-708 (with V.A. Ditkin).

[36] Vitalii Arsen'evich Ditkin (on his sixtieth birthday) (Russian). Uspehi Mat. Nauk 25 (1970), no. 5 (155), 253{258 (with A.A. Dorodnicyn, M.A. Lavrent'ev and L.A. Ljusternik). (MR 44 #2556; Zbl.201,3 and Zbl.223.01016).

[37] To the theory of operational calculus (Russian). Problems of Heat and Mass Transfers, Energija, Moscow, 1970, 317-322.

[38] Operational calculus of a class of generalized Bessel operators. Symposium on Operational Calculus and Generalized Functions, Dubrovnik, Yugoslavija, 1971, 3-11.

[39] Operational calculus of certain differential operators (Russian). Problems in applied mathematics and mechanics (dedicated to A. A. Dorodnicyn on his sixtieth birthday) (Russian), pp. 75-85, Izdat. Nauka, Moscow, 1971 (with V.A. Ditkin). (MR 58 #17702; Zbl.277.44008).

[40] One method of constructing an operational calculus (Russian). Inzh.- Fiz. Zh. 24 (1973), no. 6, 1114-1117 (with V.A. Ditkin); English transl. in J. Engrg. Phys. 24 (1975), no. 6, 778-781. (MR 52 #1195).

[41] Integral transforms and operational calculus, Second edition. Mathematical Reference Library, Vol.5. Izdat. Nauka, Moscow, 1974, 542 pp (with V.A. Ditkin). (MR 58 #29867a; Zbl.298.44007).

[42] Operational calculus, Third edition. Izdat. Vysshaja Shkola, Moscow, 1975, 467 pp (with V.A. Ditkin).

[43] On one approximate method for solving the integral equation of transfer theory (Russian). Inzh.-Fiz. Zh. 31 (1976), no. 1, 111-115 (with M.I. Zurina and A.M. Popova).

[44] Numerical solution of an integral equation of quantum mechaniccs by Pado's method (Russian). Continue Fractions and their Applications 1976; Institute of Mathematics of AN UkrSSR, Kiev, 51-52 (with M.I. Zurina and A.M. Popova).

[45] A class of multiple integrals of transfer theory (Russian). Inzh.-Fiz. Zh. 31 (1976), no. 3, 550-553 (with M.I. Zurina and A.M. Popova).

[46] Watson transform. (Russian) Mat. entsiklopedija 1977, Vol. 1, M., 510.

[47] Veber function. (Russian) Mat. entsiklopedija 1977, Vol. 1, M., 512.

[48] Integral Transfroms of Generalized Functions. Mathematical Reference Library, Izdat. Nauka, Moscow, 1977, 287 pp (with Yu.A. Brychkov). (MR 58 #2036; Zbl.464.46039).

[49] Operational calculus (Russian). Mathematical analysis, Vol. 16 (Russian), pp. 99-148; VINITI, Moscow, 1979 (with Yu.A. Brychkov and V.S. Shishov); English transl. in J. Sov. Math. 15 (1981), 733-765. (MR 80g:44010; Zbl.407.44002 and 451.44003).

[50] Transformations int egrales et calcul op erationnel (French). Editions Mir, Moscow, 1978, 435 pp (with V.A. Ditkin). (MR 58 ]29867b; ; Zbl.375.44001).

[51] Calcul op erationnel (French). Mir, Moscow, 1979, 439 pp (with V.A. Ditkin). (MR 82f:44001; Zbl.397.44001).

[52] Applicaiton of Watson operator to the solution of certain problems of the theory of heat conduction. (Russian) Inzh.-Fiz. Zh. 37 (1979), no. 3, 503-507

[53] Watson operators and their application to the solution of certain problems of the theory of heat conduction (Russian). Seminar on Numerical Methods for Solving Balance Equations (Berlin, 1980) (Russian), pp. 79{82; Rep. 1980, 5, Akad. Wiss. DDR, Berlin, 1980. (MR 82a:35052; ; Zbl.443.35036).

[54] Watson operators and some of their applications (Russian). Generalized functions and their applications in mathematical physics, Proc. Intern. Conf., M., 1980, 430-434 (with M.A. Bartoshevich). (Zbl.517.44007).

[55] Several new operational calculus formulas (Russian). Inzh.-Fiz. Zh. 41 (1981), no. 4, 727{729 (with Yu.A. Brychkov); English transl. in J. Engrg. Phys. 41 (1981), no. 4, 1160{1162. (MR 83j:44005).

[56] Integrals and Series. Elementary Functions (Russian). Nauka, Moscow, 1981, 799 pp (with Yu.A. Brychkov and O.I. Marichev). (MR 83b:00009; Zbl.511. 00044).

[57] Asymptotic behavior of the solutions of some boundary value problems for the Laplace equation in the case of deformation of the domain (Russian).Current problems in mathematics, Vol. 20, 3-36; Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1982 (with V.I. Vlasov). (MR 85c:31004; ; Zbl.523.35028 and 544.35029).

[58] Integral transformations of generalized functions (Russian). Mathematical analysis, Vol. 20 (Russian), pp. 78-115; Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, Moscow, 1982 (with Ya.A. Brychkov); English transl. in J. Sov. Math. 34 (1986), 1630-1655. (MR 84g:46062; ; Zbl.552.46021 and 595.46043).

[59] Transformations int egrales et calcul op erationnel (French). Second edition. Mir, Moscow, 1982, 435 pp (with V.A. Ditkin). (MR 85a:44001; Zbl.494.44001).

[60] Calcul op erationnel (French). Second edition. Mir, Moscow, 1983, 439 pp (with V.A. Ditkin). (MR 85a:44002)

[61] Integral transformations of generalized functions (Russian). Madrif, Baku, 1983, 246 pp (with Ya.A. Brychkov).

[62] Integrals and Series. Special Functions (Russian). Nauka, Moscow, 1983, 751 pp (with Yu.A. Brychkov and O.I. Marichev). (MR 85b:33002; Zbl.626. 00033).

[63] Certain formulas of operational calculus of two variables(Russian). Inzh.- Fiz. Zh. 44 (1983), no. 5, 814-818 (with Yu.A. Brychkov); English transl. in J. Engrg. Phys. 44 (1983), no. 5, 560-563. (MR 85j:44009).

[64] Asymptotic behavior of the solutions of some boundary value problems for the Laplace equation in the case of deformation of the domain. J. Soviet Math. 25 (1984), no. 5, 1351-1379 (with V.I. Vlasov). (MR 85c:31004).

[65] Cylindrical functions (Russian). Mat. entsiklopedija 1985, Vol. 5, M., 820-825 (with L.N.Karmazina).

[66] Tables of inde finite integrals (Russian). Nauka, Moscow, 1986, 192 pp (with Yu.A. Brychkov and O.I. Marichev). (Zbl.626.00032).

[67] A method for solving boundary value problems for the Laplace equation in domains with a curvilinear boundary (Russian). Second international symposium on complex analysis and applications (Budva, 1986); Mat. Vesnik 38 (1986), no. 4, 617-623 (with V.I. Vlasov). (MR 88i:31004; Zbl.617.31001).

[68] The Dirichlet problem for L-type domain. Complex analysis and applications '85 (Varna, 1985), 743-754, Bulg. Acad. Sci., Sofia, 1986 (with V.I. Vlasov and D.B. Volkov). (MR 88m:31003a; Zbl.628.35022).

[69] The Dirichlet problem for a circle with two notches. Complex analysis and applications '85 (Varna, 1985), 755-761, Bulg. Acad. Sci., Sofia, 1986 (with V.I. Vlasov and D.B. Volkov). (MR 88m:31003b).

[70] Torsional oscillations of the shaft with longitudinal notch Complex analysis and applications '85 (Varna, 1985), 762-766, Bulg. Acad. Sci., Sofia, 1986 (with V.I. Vlasov, D.B. Volkov and E.A. Yakovleva). (Zbl.619.73048).

[71] Integrals and Series. Supplementary Chapters (Russian). Nauka, Moscow, 1986, 800 pp (with Yu.A. Brychkov and O.I. Marichev). (MR 88f:00012; Zbl.606. 33001).

[72] Integrals and Series. Vol.1. Elementary Functions. Gordon and Breach Science Publishers, New York, 1986, 798 pp (with Yu.A. Brychkov and O.I. Marichev). (MR 88f:00013; Zbl.733.00004).

[73] Integrals and Series. Vol. 2. Special Functions. Gordon and Breach Science Publishers, New York, 1986, 750 pp (with Yu.A. Brychkov and O.I. Marichev). (MR 88f:00014 and 89i:00030; Zbl.733.00005).

[74] Solution of the Dirichlet problem in a domain with a boundary containing a rounded corner (Russian). Z. Anal. Anwendungen 6 (1987), no. 1, 61-73 (with V.I. Vlasov and D.B. Volkov). (MR 88h:35029; Zbl.645.31001).

[75] Some formulas of operational calculus for step functions generated by special functions (Russian). Inzh.-Fiz. Zh. 53 (1987), no. 6, 1010-1014 (with Yu.A. Brychkov); English transl. in J. Engrg. Phys. 53 (1987), no. 6, 1472- 1475. (MR 89f:44005).

[76] Solution of some boundary value problems in domains with a curvilinear boundary. (Russian) Problems in applied mathematics and information sciences (Russian), 169-186, Nauka, Moscow, 1987 (with V.I. Vlasov). (MR 89c:73014; Zbl.685.35034).

[77] Tables of Inde finite Integrals. Gordon and Breach Science Publishers, New York, 1989, 192 pp (with Yu.A. Brychkov and O.I. Marichev). (Zbl.728. 26001).

[78] Integral Transforms of Generalized Functions. Gordon and Breach Science Publishers, New York, 1989, 343 pp (with Yu.A. Brychkov). (MR 91e:44001; Zbl.729.46016).

[79] Calculation of integrals and the Mellin transform (Russian). Mathematical analysis, Vol. 27 (Russian), 3-146; Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1989 (with Yu.A. Brychkov and O.I. Marichev); English transl. in J. Sov. Math. 54 (1991), no. 6, 1239-1341. (MR 90m:44010; Zbl.725.44001).

[80] Vitalii Arsen'evich Ditkin (Russian). Analytical and numerical methods for solving problems in mathematical physics (Russian), 5-13, Acad. Nauk SSSR, Vychisl. Tsentr, Moscow, 1989. (MR 91j:01052a; Zbl.728.01017).

[81] A system of algorithms and programs for solving a class of boundary value problems (Russian). Analytical and numerical methods for solving problems in mathematical physics (Russian), 71-80, Acad. Nauk SSSR, Vychisl. Tsentr, Moscow, 1989 (with D.B. Volkov, V.I. Vlasov, E.A. Yakovleva
and N.Yu. Vladimirova).

[82] Integrals and Series. Vol. 3. More Special Functions. Gordon and Breach Science Publishers, New York, 1990, 800 pp (with Yu.A. Brychkov and O.I. Marichev). (MR 91c:33001).

[83] On Watson transform Fractional Calculus and its Applications, Proc. Intern. Conf. (Tokyo, 1989), 185-190; College of Engineering, Nihon University, 1990. (Zbl.751.44004).

[84] Integrals and Series. Elementary Functions (Japanese). Maruzen Co., Tokyo, 1991, 799 pp (with Yu.A. Brychkov and O.I. Marichev).

[85] Evaluation of integrals and the Mellin transform. J. Soviet Math. 54 (1991), no. 6, 1239-1341 (with Yu.A. Brychkov and O.I. Marichev).

[86] Operational calculus of perfect operators (Rusian). Acad. Nauk SSSR, Vychisl. Tsentr, Moscow, 1991, 126 pp (with I.I. Ryabtsev). (MR 93h:44008; Zbl.852.44006).

[87] Operational calculus of perfect operators (special sections) (Rusian). Ross. Acad. Nauk, Vychisl. Tsentr, Moscow, 1992, 99 pp (with I.I. Ryabtsev). (MR 95c:44003; Zbl.816.4002).

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