Generalisation of a “square” functional equation

Arjun K. Gupta

Vol. 57 (1975), No. 2, 419–422

DOI: 10.2140/pjm.1975.57.419

Abstract

Recently the difference equation defining the triangular array of binomial coefficients, known as Pascal’s triangle, has been extended to a square functional equation which generates a tableau of numbers. In the present paper these results have been generalised and the generating function for this new set of numbers has been obtained. Several relations among these numbers, which help construct the tableau, are studied. Some further generalisations of these numbers are also given.

Mathematical Subject Classification 2000

Primary: 39A10

Milestones

Received: 26 August 1974

Published: 1 April 1975