Arthur Erdélyi FRS, FRSE (October 2, 1908 – December 12, 1977) was a Hungarianborn British mathematician. Erdélyi was a leading expert on special functions  especially orthogonal polynomials and hypergeometric functions.
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Erdélyi was born in Budapest, Hungary to Ignác Diamant and Frieda Roth. He attended the primary and secondary schools there from 1914 to 1926. His interest in mathematics dates back to this time. Erdélyi was a Jew, so it was difficult for him to receive a university education in his native Hungary. He travelled to Brno, Czechoslovakia, to obtain a degree in electrical engineering. However, after his flair for mathematics was discovered (he won several prizes in a competition in his first year), he was persuaded to study the subject.
He soon after began research into the subject, and his first paper was published in 1930. At the end of 1936, he had already published 18 papers, and 11 more appeared in 1937. However, due to the German occupation of Czechoslovakia and neighbouring countries, Erdélyi was forced to flee the country.
Erdélyi contacted Edmund Whittaker, a fellow expert in hypergeometric functions for help and soon after, Erdélyi travelled to Edinburgh, Scotland, after receiving £400 for a visa from Whittaker. He joined the University of Edinburgh, and after 2 years there, became a lecturer in the Department of Mathematics (after gaining a DSc).
In 1946, after Harry Bateman died, Whittaker was asked to recommend a mathematician who could start the task of publishing Bateman's manuscripts: the Bateman Manuscript Project. Erdélyi was chosen, and in 1947, after becoming a naturalised British citizen, travelled to Caltech, California as a Visiting Professor. He returned to Edinburgh in 1948, only to resign in 1949 to assume the position of Professor of Mathematics at the California Institute. This was a post he was to hold for the next 15 years, and he retained his citizenship of Britain while in the United States.
In 1964, he returned to Edinburgh as a Professor of Mathematics, a position he held until his death in 1977.
Erdélyi was primarily an expert in special functions, in particular, Lamé functions, hypergeometric functions and orthogonal polynomials. He also contributed to the field of asymptotic analysis, fractional integration and partial differential equations. He wrote two books of high standing  Asymptotic Expansions (1955) (reprinted by Dover) and Operational Calculus and Generalised Functions (1962)
Erdélyi received several honours, including being elected to the Royal Society as a Fellow in 1975. He was also became a fellow of the Royal Society of Edinburgh in 1945, and was also elected a member of the Academy of Sciences of Turin.
