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 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 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
''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, 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&n ...
s.
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 Saunto ...
in
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. Devon is ...
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 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 down to the North Sea, and has been a majo ...
, 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 Henry VIII, King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any college at either Cambridge ...
. There he encountered
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 ...
, 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 = Â ...
. He became Professor of Pure Mathematics at the
University of Birmingham
, mottoeng = Through efforts to heights
, established = 1825 – Birmingham School of Medicine and Surgery1836 – Birmingham Royal School of Medicine and Surgery1843 – Queen's College1875 – Mason Science College1898 – Mason Univers ...
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
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 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 arbitrary ...
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 symb ...
, 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 q ...
. 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 science, natural knowledge, incl ...
,
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
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 ...
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