Arthur Erdélyi
Encyclopedia
Arthur Erdélyi FRS
, FRSE (2 October 1908 – 12 December 1977) was a Hungarian-born
British
mathematician
. Erdélyi was a leading expert on special functions
- especially orthogonal polynomials
and hypergeometric functions.
, 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.
s, hypergeometric functions and orthogonal polynomials. He also contributed to the field of asymptotic analysis
, fractional integration
and partial differential equations. He introduced the Erdélyi–Kober operators for fractional integration. He wrote two books of high standing - Asymptotic Expansions (1955) (reprinted by Dover
) and Operational Calculus and Generalised Functions (1962)
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.
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
, FRSE (2 October 1908 – 12 December 1977) was a Hungarian-born
Hungary
Hungary , officially the Republic of Hungary , is a landlocked country in Central Europe. It is situated in the Carpathian Basin and is bordered by Slovakia to the north, Ukraine and Romania to the east, Serbia and Croatia to the south, Slovenia to the southwest and Austria to the west. The...
British
Great Britain
Great Britain or Britain is an island situated to the northwest of Continental Europe. It is the ninth largest island in the world, and the largest European island, as well as the largest of the British Isles...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. Erdélyi was a leading expert on special functions
Special functions
Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications....
- especially orthogonal polynomials
Orthogonal polynomials
In mathematics, the classical orthogonal polynomials are the most widely used orthogonal polynomials, and consist of the Hermite polynomials, the Laguerre polynomials, the Jacobi polynomials together with their special cases the ultraspherical polynomials, the Chebyshev polynomials, and the...
and hypergeometric functions.
Biography
Erdélyi was born in BudapestBudapest
Budapest is the capital of Hungary. As the largest city of Hungary, it is the country's principal political, cultural, commercial, industrial, and transportation centre. In 2011, Budapest had 1,733,685 inhabitants, down from its 1989 peak of 2,113,645 due to suburbanization. The Budapest Commuter...
, Hungary
Hungary
Hungary , officially the Republic of Hungary , is a landlocked country in Central Europe. It is situated in the Carpathian Basin and is bordered by Slovakia to the north, Ukraine and Romania to the east, Serbia and Croatia to the south, Slovenia to the southwest and Austria to the west. The...
to Ignác Diamant and Frieda Roth. He attended the primary and secondary schools there from 1914 to 1926. His interest in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
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
Brno
Brno by population and area is the second largest city in the Czech Republic, the largest Moravian city, and the historical capital city of the Margraviate of Moravia. Brno is the administrative centre of the South Moravian Region where it forms a separate district Brno-City District...
, Czechoslovakia
Czechoslovakia
Czechoslovakia or Czecho-Slovakia was a sovereign state in Central Europe which existed from October 1918, when it declared its independence from the Austro-Hungarian Empire, until 1992...
, to obtain a degree in electrical engineering
Electrical engineering
Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...
. 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
Edinburgh
Edinburgh is the capital city of Scotland, the second largest city in Scotland, and the eighth most populous in the United Kingdom. The City of Edinburgh Council governs one of Scotland's 32 local government council areas. The council area includes urban Edinburgh and a rural area...
, Scotland
Scotland
Scotland is a country that is part of the United Kingdom. Occupying the northern third of the island of Great Britain, it shares a border with England to the south and is bounded by the North Sea to the east, the Atlantic Ocean to the north and west, and the North Channel and Irish Sea to the...
, after receiving £
Pound sterling
The pound sterling , commonly called the pound, is the official currency of the United Kingdom, its Crown Dependencies and the British Overseas Territories of South Georgia and the South Sandwich Islands, British Antarctic Territory and Tristan da Cunha. It is subdivided into 100 pence...
400 for a visa from Whittaker. He joined the University of Edinburgh
University of Edinburgh
The University of Edinburgh, founded in 1583, is a public research university located in Edinburgh, the capital of Scotland, and a UNESCO World Heritage Site. The university is deeply embedded in the fabric of the city, with many of the buildings in the historic Old Town belonging to the university...
, and after 2 years there, became a lecturer in the Department of Mathematics (after gaining a DSc).
In 1946, after Harry Bateman
Harry Bateman
Harry Bateman FRS was an English mathematician.-Life and work:Harry Bateman first grew to love mathematics at Manchester Grammar School, and in his final year, won a scholarship to Trinity College, Cambridge. There he distinguished himself in 1903 as Senior Wrangler and by winning the Smith's Prize...
died, Whittaker was asked to recommend a mathematician who could start the task of publishing Bateman's manuscripts: the Bateman Manuscript Project
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 Arthur Erdélyi....
. Erdélyi was chosen, and in 1947, after becoming a naturalised British citizen, travelled to Caltech, California
California
California is a state located on the West Coast of the United States. It is by far the most populous U.S. state, and the third-largest by land area...
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.
Research
Erdélyi was primarily an expert in special functions, in particular, Lamé functionLamé function
In mathematics, a Lamé function is a solution of Lamé's equation, a second-order ordinary differential equation. It was introduced in the paper . Lamé's equation appears in the method of separation of variables applied to the Laplace equation in elliptic coordinates...
s, hypergeometric functions and orthogonal polynomials. He also contributed to the field of asymptotic analysis
Asymptotic analysis
In mathematical analysis, asymptotic analysis is a method of describing limiting behavior. The methodology has applications across science. Examples are...
, fractional integration
Fractional calculus
Fractional calculus is a branch of mathematical analysis that studies the possibility of taking real number powers or complex number powers of the differentiation operator.and the integration operator J...
and partial differential equations. He introduced the Erdélyi–Kober operators for fractional integration. He wrote two books of high standing - Asymptotic Expansions (1955) (reprinted by Dover
Dover
Dover is a town and major ferry port in the home county of Kent, in South East England. It faces France across the narrowest part of the English Channel, and lies south-east of Canterbury; east of Kent's administrative capital Maidstone; and north-east along the coastline from Dungeness and Hastings...
) and Operational Calculus and Generalised Functions (1962)
Awards
Erdélyi received several honours, including being elected to the Royal SocietyRoyal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
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.