# G. N. Watson

Prof **George Neville Watson** FRS HFRSE LLD (31 January 1886 – 2 February 1965) was an English mathematician, who applied complex analysis to the theory of special functions. His collaboration on the 1915 second edition of E. T. Whittaker's *A Course of Modern Analysis* (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 integrals.[1][3][4]

G. N. Watson | |
---|---|

Born | George Neville Watson 31 January 1886 |

Died | 2 February 1965 79) Leamington Spa, Warwickshire | (aged

Nationality | United Kingdom |

Alma mater | Trinity College, Cambridge |

Known for | Whittaker and Watson text Watson's quintuple product identity |

Awards | Smith's Prize (1909) Sylvester Medal (1946) De Morgan Medal (1947) Fellow of the Royal Society[1] |

Scientific career | |

Fields | mathematics |

Institutions | University of Birmingham University of Cambridge |

Doctoral advisor | E. T. Whittaker[2] |

## 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.[5]

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.[6]

He was awarded an honorary MSc Pure Science in 1919 by Birmingham University.[7]

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)[8] 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 functions[9] and q-series, and for some time looked after Ramanujan's lost notebook.

Sometime in the late 1920s, G. N. Watson and B. M. Wilson began the task of editing Ramanujan's notebooks. The second notebook, being a revised, enlarged edition of the first, was their primary focus. Wilson was assigned Chapters 2–14, and Watson was to examine Chapters 15–21. Wilson devoted his efforts to this task until 1935, when he died from an infection at the early age of 38. Watson wrote over 30 papers inspired by the notebooks before his interest evidently waned in the late 1930s.[10]

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.[11]

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,[1] and in 1946, he received the Sylvester Medal 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.[12]

## References

- Whittaker, J. M. (1966). "George Neville Watson 1886-1965".
*Biographical Memoirs of Fellows of the Royal Society*.**12**: 520–526. doi:10.1098/rsbm.1966.0026. - G. N. Watson at the Mathematics Genealogy Project
- Rankin, R. A. (1966). "George Neville Watson".
*Journal of the London Mathematical Society*. s1-41: 551–565. doi:10.1112/jlms/s1-41.1.551. - O'Connor, John J.; Robertson, Edmund F., "G. N. Watson",
*MacTutor History of Mathematics archive*, University of St Andrews. -
*Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002*(PDF). The Royal Society of Edinburgh. July 2006. ISBN 978-0-902198-84-5. -
*Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002*(PDF). The Royal Society of Edinburgh. July 2006. ISBN 978-0-902198-84-5. - "University campus Blue Plaque Trail". Birmingham University. Retrieved 12 November 2014.
- Carmichael, R. D. (1924). "Review:
*A Treatise on the Theory of Bessel Functions*, by G. N. Watson".*Bull. Amer. Math. Soc*.**30**(7): 362–364. doi:10.1090/s0002-9904-1924-03906-8. - Watson, G. N. (1937). "The mock theta functions (2)".
*Proceedings of the London Mathematical Society*.**2**(1): 274–304. doi:10.1112/plms/s2-42.1.274. - Berndt, Bruce C. "An overview of Ramanujan's notebooks" (PDF).
*math.uiuc.edu/~berndt/articles/aachen.pdf*. p. 3; paper delivered at Proc. Conf. Karl der Grosse - Adiga, B.; Berndt, B. C.; Bhargava, S.; Watson, G. N. (1985),
*Ramanujan's second notebook: Theta-functions and q-series Chap. 16*,**53**, Providence, Rhode Island: Amer. Math. Soc., pp. 1–85 - http://www-history.mcs.st-and.ac.uk/Obits2/Watson_RSE_Obituary.html