by P. M. Cohn

© Oxford University Press 2004 All rights reserved

**Ince, Edward Lindsay** (1891-1941), mathematician, was born on 30 November 1891 in King William Street, Amblecote, Staffordshire, the only son of Edward Ince, an Inland Revenue officer, and his wife, Caroline Clara Cutler. He attended Cricieth School and the county school at Portmadoc, and, after his family moved to Scotland, completed his secondary education at the Perth Academy. In 1909 he went to Edinburgh University to read mathematics, and graduated in 1913 with first-class honours. He played a prominent part in the communal life of the university as senior president of the students' representative council and convener of the international academic committee. A scholarship awarded to him on graduation enabled him to remain in Edinburgh for research. After being rejected for war service on medical grounds, he entered Trinity College, Cambridge, in 1915 as research student, and was a Smith's prizeman in 1917, but after four terms left for a national service appointment.

In 1924 Ince married Phyllis Fry, with whom he had two daughters. After the war he held lectureships, first at Leeds and then in 1920-26 in Liverpool. In 1926 he was elected to the chair in pure mathematics at the newly founded Egyptian University, Cairo. Building up a new department was congenial to him and he proved a most successful teacher and organizer, but in 1931 he decided to return to Britain because of lack of facilities for educating his children and the effect of the climate on his health. After spending the session 1931-2 as lecturer in Edinburgh, and 1932-5 at Imperial College, London, he returned to Edinburgh as head of the department for technical mathematics, where he remained until his death.

Ince's main work was in the theory of differential equations. E. L. Mathieu in 1868 had, in the study of vibrations of an elliptic membrane, introduced and solved the differential equation now bearing his name, but a thorough study, using modern function-theoretic methods, was only beginning when Ince graduated; he was to make important contributions to the theory of Mathieu equations, proving the uniqueness of periodic solutions, now called Mathieu functions, and extending this work to Hill's equation. He found that the equation admits a solution of period π or 2π for certain values of a parameter, the 'eigenvalues'. A knowledge of these eigenvalues is prerequisite for numerical computations with Mathieu functions; Ince felt that providing tables of these values for physicists and astronomers was essential, though he realized that a practicable method of construction depended on progress in theoretical analysis. By the use of convergent infinite determinants and continued fractions, with asymptotic formulae for large values, he succeeded in making computations practicable and after eight years' devotion to this task he published in 1932 tables of eigenvalues for Mathieu's equation, and zeros of Mathieu functions. These tables were useful not only in the problems originally envisaged but also in more recent investigations such as quantum-mechanical problems leading to Mathieu's equation.

Ince's interests extended over a large part of analysis, and he put this to good use in his book *Ordinary Differential Equations,* which gave a modern presentation of the theory, using methods from algebra as well as analysis. Published in 1927, it immediately became a classic and remained in print for many years. In two papers published in the last year of his life he made important contributions to the theory of Lamé's equation; in particular he introduced orthogonal functions for their expansions, thus simplifying and extending results of previous authors.

In 1923 Ince was elected fellow of the Royal Society of Edinburgh; he was awarded its Makdougall Brisbane prize but did not live to receive the award. He was also a member of the London Mathematical Society and of the Royal Astronomical Society. He died of leukaemia at St Raphael's Home, Blackford Avenue, Edinburgh, on 16 March 1941. He was survived by his wife.

P. M. COHN

**Sources **

*WWW*

E. T. Whittaker, *Journal of the London Mathematical Society,* 16 (1941), 139-44

A. W. Y. [A. W. Young], *Year Book of the Royal Society of Edinburgh* (1940-41), 18

b. cert.

d. cert.

**Wealth at death **

£4023 *2s. 4d.:* confirmation, 11 June 1941, *CCI*

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