Neville Watson (31 January 1886 – 2 February 1965) was an English

English people

The English are a nation and ethnic group native to England, who speak English. The English identity is of early mediaeval origin, when they were known in Old English as the Anglecynn. England is now a country of the United Kingdom, and the majority of English people in England are British Citizens...

 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....

, a noted master in the application of complex analysis

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 useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...

 to the theory of special functions. His collaboration on the 1915 second edition of E. T. Whittaker

E. T. Whittaker

Edmund Taylor Whittaker FRS FRSE was an English mathematician who contributed widely to applied mathematics, mathematical physics and the theory of special functions. He had a particular interest in numerical analysis, but also worked on celestial mechanics and the history of physics...

's A Course of Modern Analysis (1902) produced the classic “Whittaker & Watson” text. In 1918 he proved a significant result known as Watson's lemma

Watson's lemma

In mathematics, Watson's lemma, proved by G. N. Watson , has significant application within the theory on the asymptotic behavior of integrals.- Statement of the lemma :...

, that has many applications in the theory on the asymptotic behavior of exponential

Exponential function

In mathematics, the exponential function is the function ex, where e is the number such that the function ex is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change In mathematics,...

 integrals.

His Treatise on the theory of Bessel functions (1922) was a virtuoso display, in particular in the asymptotic expansion

Asymptotic expansion

In mathematics an asymptotic expansion, asymptotic series or Poincaré expansion is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation to a given function as the argument of the function tends towards a particular,...

s of Bessel function

Bessel function

In mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y of Bessel's differential equation:...

s. It also became a classic.

He subsequently spent many years on Ramanujan's formulae in the area of complex multiplication

Complex multiplication

In mathematics, complex multiplication is the theory of elliptic curves E that have an endomorphism ring larger than the integers; and also the theory in higher dimensions of abelian varieties A having enough endomorphisms in a certain precise sense In mathematics, complex multiplication is the...

, mock theta function

Mock theta function

In mathematics, a mock modular form is the holomorphic part of a harmonic weak Maass form, anda mock theta function is essentially a mock modular form of weight 1/2. The first examples of mock theta functions were described by Srinivasa Ramanujan in his last 1920 letter to G. H. Hardy and in his...

s and class numbers, and for some time looked after Ramanujan's lost notebook

Ramanujan's lost notebook

Srinivasa Ramanujan's lost notebook is the manuscript in which Ramanujan, the great Indian mathematician from Cambridge University, recorded the mathematical discoveries of the last year of his life. It was rediscovered by George Andrews in 1976, in a box of effects of G. N. Watson stored at the...

.
His interests included solvable cases of the quintic equation

Quintic equation

In mathematics, a quintic function is a function of the formg=ax^5+bx^4+cx^3+dx^2+ex+f,\,where a, b, c, d, e and f are members of a field, typically the rational numbers, the real numbers or the complex numbers, and a is nonzero...

. He introduced Watson's quintuple product identity.

He was educated at St Paul's School, as a pupil of F. S. Macaulay, and Trinity College, Cambridge

Trinity College, Cambridge

Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...

. There he encountered Whittaker, though their overlap was only two years. He became Professor at the University of Birmingham

University of Birmingham

The University of Birmingham is a British Redbrick university located in the city of Birmingham, England. It received its royal charter in 1900 as a successor to Birmingham Medical School and Mason Science College . Birmingham was the first Redbrick university to gain a charter and thus...

 in 1918, where he remained until 1951.

Watson was elected to the Royal Society

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"...

, and in 1946, he received the Sylvester Medal

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...

 from the Society.

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