George Neville Watson (31 January 1886 – 2 February 1965) was an English mathematician, who applied

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...

to the theory of special functions. His collaboration on the 1915 second edition of E. T. Whittaker's ''

A Course of Modern Analysis ''A Course of Modern Analysis: an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions'' (colloquially known as Whittaker and Watson) is a landmark textb ...

'' (1902) produced the classic "

Whittaker and Watson ''A Course of Modern Analysis: an introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions'' (colloquially known as Whittaker and Watson) is a landmark textb ...

" text. In 1918 he proved a significant result known as

Watson's lemma In mathematics, Watson's lemma, proved by G. N. Watson (1918, p. 133), has significant application within the theory on the asymptotic behavior of integrals. Statement of the lemma Let 0 -1. Suppose, in addition, either that :, \varphi(t), ...

, that has many applications in the theory on the asymptotic behaviour of exponential integrals.

Life

He was born in Westward Ho! in Devon the son of George Wentworth Watson, a schoolmaster and genealogist, and his wife, Mary Justina Griffith. He was educated at St Paul's School in London, as a pupil of F. S. Macaulay. He then studied Mathematics at Trinity College, Cambridge. There he encountered E. T. Whittaker, though their overlap was only two years. From 1914 to 1918 he lectured in Mathematics at University College, London. He became Professor of Pure Mathematics at the University of Birmingham in 1918, replacing Prof R S Heath, and remained in this role until 1951. He was awarded an

honorary An honorary position is one given as an honor, with no duties attached, and without payment. Other uses include: * Honorary Academy Award, by the Academy of Motion Picture Arts and Sciences, United States * Honorary Aryan, a status in Nazi Germany ...

MSc Pure Science in 1919 by Birmingham University. He was President of the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

1933/35. He died at

Leamington Spa Royal Leamington Spa, commonly known as Leamington Spa or simply Leamington (), is a spa town and civil parish in Warwickshire, England. Originally a small village called Leamington Priors, it grew into a spa town in the 18th century following ...

on 2 February 1965.

Works

His ''Treatise on the theory of Bessel functions'' (1922) also became a classic, in particular in regard to the asymptotic expansions of Bessel functions. He subsequently spent many years on Ramanujan's formulae in the area of modular equations,

mock theta function In mathematics, a mock modular form is the holomorphic part of a harmonic weak Maass form, and a mock theta function is essentially a mock modular form of weight . The first examples of mock theta functions were described by Srinivasa Ramanujan ...

s and

q-series In mathematical area of combinatorics, the ''q''-Pochhammer symbol, also called the ''q''-shifted factorial, is the product (a;q)_n = \prod_^ (1-aq^k)=(1-a)(1-aq)(1-aq^2)\cdots(1-aq^), with (a;q)_0 = 1. It is a ''q''-analog of the Pochhammer symb ...

, and for some time looked after Ramanujan's lost notebook. Ramanujan discovered many more modular equations than all of his mathematical predecessors combined. Watson provided proofs for most of Ramanujan's modular equations. Bruce C. Berndt completed the project begun by Watson and Wilson. Much of Berndt's book ''Ramanujan's Notebooks, Part 3'' (1998) is based upon the prior work of Watson. Watson's interests included solvable cases of the quintic equation. He introduced Watson's quintuple product identity.

Honours and awards

In 1919 Watson was elected a Fellow of the Royal Society, and in 1946, he received the Sylvester Medal from the Society. He was president of the

from 1933 to 1935. He is sometimes confused with the mathematician G. L. Watson, who worked on quadratic forms, and G. Watson, a statistician.

Family

In 1925 he married Elfrida Gwenfil Lane daughter of Thomas Wright Lane.

References

{{DEFAULTSORT:Watson, George Neville 1886 births 1965 deaths People from Bideford 20th-century English mathematicians Mathematical analysts People educated at St Paul's School, London Academics of the University of Birmingham Senior Wranglers Fellows of the Royal Society De Morgan Medallists Alumni of Trinity College, Cambridge