Arthur Erdélyi FRS,

FRSE Fellowship of the Royal Society of Edinburgh (FRSE) is an award granted to individuals that the Royal Society of Edinburgh, Scotland's national academy of science and Literature, letters, judged to be "eminently distinguished in their subject". ...

(2 October 1908 – 12 December 1977) was a Hungarian-born

British British may refer to: Peoples, culture, and language * British people, nationals or natives of the United Kingdom, British Overseas Territories and Crown Dependencies. * British national identity, the characteristics of British people and culture ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. Erdélyi was a leading expert on

special functions Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined by ...

, particularly

orthogonal polynomials In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal In mathematics, orthogonality (mathematics), orthogonality is the generalization of the geom ...

and

hypergeometric function In mathematics, the Gaussian or ordinary hypergeometric function 2''F''1(''a'',''b'';''c'';''z'') is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is ...

Biography

He was born Arthur Diamant in

Budapest Budapest is the Capital city, capital and List of cities and towns of Hungary, most populous city of Hungary. It is the List of cities in the European Union by population within city limits, tenth-largest city in the European Union by popul ...

Hungary Hungary is a landlocked country in Central Europe. Spanning much of the Pannonian Basin, Carpathian Basin, it is bordered by Slovakia to the north, Ukraine to the northeast, Romania to the east and southeast, Serbia to the south, Croatia and ...

to Ignác Josef Armin Diamant and Frederike Roth. His name was changed to Erdélyi when his mother remarried to Paul Erdélyi. He attended the primary and secondary schools there from 1914 to 1926. His interest in

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

dates back to this time. Erdélyi was a

Jew Jews (, , ), or the Jewish people, are an ethnoreligious group and nation, originating from the Israelites of ancient Israel and Judah. They also traditionally adhere to Judaism. Jewish ethnicity, religion, and community are highly inte ...

, and so it was difficult for him to receive a university education in his native Hungary. He travelled to

Brno Brno ( , ; ) is a Statutory city (Czech Republic), city in the South Moravian Region of the Czech Republic. Located at the confluence of the Svitava (river), Svitava and Svratka (river), Svratka rivers, Brno has about 403,000 inhabitants, making ...

Czechoslovakia Czechoslovakia ( ; Czech language, Czech and , ''Česko-Slovensko'') was a landlocked country in Central Europe, created in 1918, when it declared its independence from Austria-Hungary. In 1938, after the Munich Agreement, the Sudetenland beca ...

, to obtain a degree in

electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems that use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

. 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 to conduct theoretical research into mathematics, 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, asking for his assistance and soon after, Erdélyi travelled to

Edinburgh Edinburgh is the capital city of Scotland and one of its 32 Council areas of Scotland, council areas. The city is located in southeast Scotland and is bounded to the north by the Firth of Forth and to the south by the Pentland Hills. Edinburgh ...

Scotland Scotland is a Countries of the United Kingdom, country that is part of the United Kingdom. It contains nearly one-third of the United Kingdom's land area, consisting of the northern part of the island of Great Britain and more than 790 adjac ...

, after receiving £400 for a visa from Whittaker. He joined the

University of Edinburgh The University of Edinburgh (, ; abbreviated as ''Edin.'' in Post-nominal letters, post-nominals) is a Public university, public research university based in Edinburgh, Scotland. Founded by the City of Edinburgh Council, town council under th ...

, and after 2 years there, became a lecturer in the Department of Mathematics (after gaining a DSc in 1940 based on his already extensive published work). In 1946, after

Harry Bateman Harry Bateman FRS (29 May 1882 – 21 January 1946) was an English mathematician with a specialty in differential equations of mathematical physics. With Ebenezer Cunningham, he expanded the views of spacetime symmetry of Lorentz and Poinca ...

died, Whittaker was asked to recommend a mathematician who could start the task of publishing Bateman's manuscripts: the

Bateman Manuscript Project The Bateman Manuscript Project was a major effort at collation and encyclopedic compilation of the mathematical theory of special functions. It resulted in the eventual publication of five important reference volumes, under the editorship of Arth ...

. Erdélyi was chosen, and in 1947, after becoming a naturalised British

citizen Citizenship is a membership and allegiance to a sovereign state. Though citizenship is often conflated with nationality in today's English-speaking world, international law does not usually use the term ''citizenship'' to refer to nationality ...

, travelled to

Caltech The California Institute of Technology (branded as Caltech) is a private university, private research university in Pasadena, California, United States. The university is responsible for many modern scientific advancements and is among a small g ...

California California () is a U.S. state, state in the Western United States that lies on the West Coast of the United States, Pacific Coast. It borders Oregon to the north, Nevada and Arizona to the east, and shares Mexico–United States border, an ...

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 of Technology. 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. He died in Edinburgh.

Family

He married Eva Neuburg in 1942. They did not have children.

Research

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 In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing Limit (mathematics), limiting behavior. As an illustration, suppose that we are interested in the properties of a function as becomes very larg ...

fractional integration In fractional calculus, an area of mathematical analysis, the differintegral is a combined differentiation/integration operator. Applied to a function ƒ, the ''q''-differintegral of ''f'', here denoted by :\mathbb^q f is the fractional derivat ...

and

partial differential equations In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to how ...

. He introduced the Erdélyi–Kober operators for

. He wrote two books of high standing - ''Asymptotic Expansions (1955)'' (reprinted by

Dover Dover ( ) is a town and major ferry port in Kent, southeast England. It faces France across the Strait of Dover, the narrowest part of the English Channel at from Cap Gris Nez in France. It lies southeast of Canterbury and east of Maidstone. ...

) and ''Operational Calculus and Generalised Functions (1962)''

Works

*

https://resolver.caltech.edu/CaltechAUTHORS:20140123-104529738] (xxvi+4 errata pages+302 pages) (NB. With a preface by

Mina Rees Mina Spiegel Rees (August 2, 1902 – October 25, 1997) was an American mathematician. She is known for her assistance to the US Government during WWII, as well as making several breakthroughs for women in science. Her most notable accomplishment ...

and a foreword by Earnest C. Watson. Copyright was renewed by

California Institute of Technology The California Institute of Technology (branded as Caltech) is a private research university in Pasadena, California, United States. The university is responsible for many modern scientific advancements and is among a small group of institutes ...

in 1981.); Reprint: Robert E. Krieger Publishing Co., Inc., Melbourne, Florida, USA. 1981. ; Planned Dover reprint . *

https://resolver.caltech.edu/CaltechAUTHORS:20140123-104529738] (xvii+1 errata page+396 pages) (NB. Copyright was renewed by

in 1981.); Reprint: Robert E. Krieger Publishing Co., Inc., Melbourne, Florida, USA. 1981. ; Planned Dover reprint: . *

https://resolver.caltech.edu/CaltechAUTHORS:20140123-104529738] (xvii+292+2 pages) (NB. Copyright was renewed by

in 1983.); Reprint: Robert E. Krieger Publishing Co., Inc., Melbourne, Florida, USA. 1981. ; Planned Dover reprint . *

(xx+391 pages including 1 errata page, red cloth hardcover) *

(xvi+451 pages, red cloth hardcover) * (vi+108 pages) * (iii+137 pages) * (viii+103 pages)

Awards

Erdélyi received several honours, including being elected to the

Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...

as a Fellow in 1975. He 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.

References

{{DEFAULTSORT:Erdelyi, Arthur 1908 births 1977 deaths Mathematicians from Budapest Hungarian Jews Jews who immigrated to the United Kingdom to escape Nazism Fellows of the Royal Society Fellows of the Royal Society of Edinburgh California Institute of Technology faculty Academics of the University of Edinburgh 20th-century British mathematicians Hungarian refugees Hungarian expatriates in Czechoslovakia Hungarian emigrants to the United Kingdom