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

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 mathema ...

'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 ...

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 known as Devonshire , ) is a ceremonial and non-metropolitan county in South West England. The most populous settlement in Devon is the city of Plymouth, followed by Devon's county town, the city of Exeter. Devo ...

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 and List of urban areas in the United Kingdom, largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary dow ...

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

Trinity College, Cambridge Trinity College is a 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 college at either Cambridge or Oxford. ...

. There he encountered

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

University College, London , mottoeng = Let all come who by merit deserve the most reward , established = , type = Public research university , endowment = £143 million (2020) , budget = � ...

. 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 located in Edgbaston, Birmingham, United Kingdom. It received its royal charter in 1900 as a successor to Queen's College, Birmingha ...

in 1918, replacing Prof R S Heath, and remained in this role until 1951. He was awarded an honorary MSc Pure Science in 1919 by Birmingham University. He was President of the London Mathematical Society 1933/35. He died at Leamington Spa 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 to ...

s of

Bessel function Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrar ...

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 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 Ramanu ...

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 sym ...

, 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 Bruce Carl Berndt (born March 13, 1939, in St. Joseph, Michigan) is an American mathematician. Berndt attended college at Albion College, graduating in 1961, where he also ran track. He received his master's and doctoral degrees from the Universi ...

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 algebra, 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 words, a ...

. 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 judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural knowledge, including mathemat ...

, and in 1946, he received the

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

from the Society. He was president of the London Mathematical Society 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