A Note on the form of Jacobi Polynomial used in Harish-Chandra’s Paper ‘Motion of an Electron in the Field of a Magnetic Pole’

Abstract

It is very interesting and difficult to understand the papers of the great mathematician Prof. Harish-Chandra (1923-1983). While reading any one of them the reader is compelled to know the answers of many questions standing on the way. We have tried to understand his paper1 and found that the Jacobi polynomial appears on the way of solution of wave equation of electron moving in the field of a magnetic pole. This Jacobi polynomial is not in the usual form appearing in mathematical literature. In this paper we have compared the Jacobi polynomial used by Harish-Chandra with its usual form. We have also deduced the explicit form for such polynomials from identity given in his paper. We have also verified the results found by him concerning Jacobi polynomials