On Generalised heat Polynomials

Abstract

The present paper is concerned with a polynomial set associated with generalised heat polynomial 'due to D. T. Haimo (1966). Associated polynomial set hat been subjected to further investigations and several properties. such as explicit form, finite, summation formula, generating'Neictioi41-44d.) bilateral generating functions, have been established. The: paper has been concluded by giving some series relations for generalised heat polynomials in terms of circular, hyperbolic and hypergeometric functions. The corresponding results for the ordinary heat polynomials of even order defined' by. P.C. Rosenbloom and D.V.Widder (1959) and the Hermite polynomials of even order are rendered intuitive.