Mathematical and Physical Sciences

Abstract

FROM 1873 onwards, at irregular intervals, the British Association has published in its annual report various mathematical tables. Unfortunately, these were generally compiled for special purposes, and when regarded as a whole were not well suited for general use. To remedy this defect a committee undertook the heavy task of filling the gaps and (a point altogether neglected in the original form) making them suitable for interpolation. The first volume, begun by R. A. Fisher and completed by J. Henderson, with the assistance of J. R. Airey, L. J. Comrie, A. T. Doodson, A. Lodge, J. Wishart, and others, contains sixteen tables. Some of these are new, and two of them (dealing with tetra-gamma and pentagamma functions) are the only tables of these functions in existence. The degree of accuracy is high, extending (except in the last) from ten to fifteen decimal places. There is an elaborate introduction filling thirty pages, beginning with interpolation, using Everett's formula and central differences of even orders, for which these tables are specially suitable. After a brief treatment of the better-known functions, the introduction concludes with an extensive account of the properties of certain probability repeated integrals (really Hermite functions) and their applications to statistics.