On a “square” functional equation

Arjun K. Gupta

Vol. 50 (1974), No. 2, 449–454

DOI: 10.2140/pjm.1974.50.449

Abstract

In a recent paper Stanton and Cowan have generalized the Pascal’s triangle to a tableau. They have developed several expressions for these numbers, using combinatorial techniques. In the present paper we derive some of their results very simply, by using the calculus of finite differences. We further obtain the relations of these numbers to hypergeometric function and derive many relations among these numbers which are useful in constructing the tableau.

Mathematical Subject Classification 2000

Primary: 39A10

Milestones

Received: 5 October 1972

Published: 1 February 1974