SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

Memorial Note about Vasily Borisovich Uvarov (1929 - 1997)

The distinguished Russian mathematician and physicist Vasily Borisovich Uvarov died on 23rd of September 1997, four days after his 68th birthday. A flamboyant personality of splendid health, he suddenly contracted Alzheimer's disease about 5 years ago, but died in hospital from pneumonia.

Born into an old and cultivated Muscovite family, he graduated cum laude in 1952 from the Physics Department of Moscow State University. For the rest of his life, he worked at the M. V. Keldysh Institute of Applied Mathematics. During his last years he was head researcher at the Institute and professor at MSU.

When starting his work at the Institute, Uvarov entered the Ippolitov-Ivanov Moscow Musical School as a student of violin and soon graduated from the School. He played the violin throughout his life. As a joke he used to say that, playing the violin, he could compete with Einstein.

Research in the domain of high-temperature plasma physics (to be more precise, in domain of quantum statistical models and interaction of radiation with matter), started in the late 1950s. At that time computers were only at the very beginning of their development, so the researcher had to know how to obtain analytical solutions of rather complicated sets of differential equations and, more specifically, had to be proficient in the art of dealing with many special functions. Full control both of analytical and difference methods enabled Uvarov to solve the problem of photon absorption in spectral lines of many-electron atoms. In 1962 V.B. Uvarov received the country's highest scientific award - the Lenin prize.

Later, Uvarov and Nikiforov developed a new approach to the theory of special functions using a generalization of the Rodrigues formula. They succeeded in obtaining, in the form of a Cauchy integral, a unified integral representation for functions of hypergeometric type (1974). The later book Special Functions of Mathematical Physics was based on these ideas and went through several editions in Russian, French and English. The latest edition was translated into English by the famous American mathematician Ralph Boas (1988).

In 1983 it came to be recognized that along with the differential equation of hypergeometric type one has to introduce the difference equation of hypergeometric type over nonuniform lattices for many functions, given on discrete sets of argument values. The polynomial solutions of this equation (so-called q-polynomials) were obtained, investigated and classified in collaboration with A. F. Nikiforov and S. K. Suslov in the book Classical Orthogonal Polynomials of a Discrete Variable (Moscow, Nauka, 1985; Springer-Verlag, 1991). This plan has been carried out independently by the American mathematicians R. Askey and J. A. Wilson.

Many-sidedly talented and wonderfully modest, sometimes unyielding, - this is how Vasily Borisovich Uvarov will stay in our memory.

Arnold Nikiforov

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