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 functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...

to the theory of

special function 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 ...

s. His collaboration on the 1915 second edition of

E. T. Whittaker Sir Edmund Taylor Whittaker (24 October 1873 – 24 March 1956) was a British mathematician, physicist, and historian of science. Whittaker was a leading mathematical scholar of the early 20th century who contributed widely to applied mathemat ...

'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" text. In 1918 he proved a significant result known as Watson's lemma, that has many applications in the theory on the asymptotic behaviour of

exponential integral In mathematics, the exponential integral Ei is a special function on the complex plane. It is defined as one particular definite integral of the ratio between an exponential function and its argument. Definitions For real non-zero values of&nb ...

Life

He was born in

Westward Ho! Westward Ho! is a seaside village near Bideford in Devon, England. The A39 road provides access from the towns of Barnstaple, Bideford, and Bude. It lies at the south end of Northam Burrows and faces westward into Bideford Bay, opposite Sau ...

Devon Devon ( ; historically also known as Devonshire , ) is a ceremonial county in South West England. It is bordered by the Bristol Channel to the north, Somerset and Dorset to the east, the English Channel to the south, and Cornwall to the west ...

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 London is the Capital city, capital and List of urban areas in the United Kingdom, largest city of both England and the United Kingdom, with a population of in . London metropolitan area, Its wider metropolitan area is the largest in Wester ...

, as a pupil of F. S. Macaulay. He then studied Mathematics at

Trinity College, Cambridge Trinity College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any ...

. There he encountered

, though their overlap was only two years. From 1914 to 1918 he lectured in Mathematics at

University College, London University College London (Trade name, branded as UCL) is a Public university, public research university in London, England. It is a Member institutions of the University of London, member institution of the Federal university, federal Uni ...

. He became Professor of Pure Mathematics at the

University of Birmingham The University of Birmingham (informally Birmingham University) is a Public university, public research university in Birmingham, England. It received its royal charter in 1900 as a successor to Queen's College, Birmingham (founded in 1825 as ...

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 society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh ...

1933/35. He died at

Leamington Spa Royal Leamington Spa, commonly known as Leamington Spa or simply LeamingtonEven more colloquially, also referred to as Lem or Leam (). (), is a spa town and civil parish in Warwickshire, England. Originally a small village called Leamington Pri ...

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 expansion In mathematics, an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation ...

s of

Bessel function Bessel functions, named after Friedrich Bessel who was the first to systematically study them in 1824, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary complex ...

s. 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 function, holomorphic part of a harmonic weak Maass wave form, Maass form, and a mock theta function is essentially a mock modular form of weight . The first examples of mock theta functions ...

s and

q-series In the mathematical field 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 Pochhamme ...

, and for some time looked after

Ramanujan's lost notebook Ramanujan's lost notebook is the manuscript in which the Indian mathematician Srinivasa Ramanujan recorded the mathematical discoveries of the last year (1919–1920) of his life. Its whereabouts were unknown to all but a few mathematicians until i ...

. 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 In mathematics, a quintic function is a function of the form :g(x)=ax^5+bx^4+cx^3+dx^2+ex+f,\, where , , , , and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero. In other word ...

. He introduced Watson's quintuple product identity.

Honours and awards

In 1919 Watson was elected a

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the Fellows of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

, and in 1946, he received the

Sylvester Medal The Sylvester Medal is a bronze medal awarded by the Royal Society for the encouragement of mathematical research, and accompanied by a £1,000 prize. It was named in honour of James Joseph Sylvester, the Savilian chair of geometry, Savilian Prof ...

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 Mathematics education in the United Kingdom 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