Mathematics

Abstract

THE ordinary hypergeometric series, discussed by Gauss about a century ago, is well known; it is a function of three parameters, of which two occur in the numerator and one in the denominator. In the generalised series, the number of the parameters in the numerator and denominator may be anything we please. Until comparatively recently, it was difficult to obtain anything like a complete grasp of the scattered work on these series. Cay ley, in 1858, published, without proof, a theorem which he had inferred from considerations of planetary theory, and it was not until forty-one years later that a proof was discovered (by W. McF. Orr). Ramanujan rediscovered for himself many results already known but not accessible to him. The first systematic account of the subject was contained in Hardy's paper, “A Chapter from Ramanujan's Note-book” (1923). Since then numerous papers have been published, and at the suggestion of Prof. L. J. Mordell this tract, dealing largely with recent work, has been prepared by Dr. Bailey, who has himself played a leading part in the development of the subject.

Generalized Hypergeometric Series

By Dr. W. N. Bailey (Cambridge Tracts in Mathematics and Mathematical Physics, No. 32.) Pp. vi + 108. (Cambridge: At the University Press, 1935.) 6s. 6d. net.