A study of polynomials associated with some generating functions

Author

Son N. Luong

Date of Award

12-1989

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

Kusum Soni

Committee Members

Yueh-er Kuo, Julius Smith

Abstract

Many familiar polynomials such as the Hermite polynomials and the Appell polynomials have the generating functions of the form

F(x,t)=A(t)G(xt)=^∞_n=0∑g_n(x)tⁿ.

We say that F(x,t) generates the sequence of polynomials {g_n(x)} and that F(x,t) is a generating function for the g_n(x).

The purpose of this paper is to develop some properties of the polynomials g_n(x) associated with certain choices of A(t). These will include some recurrence relations which follow from a partial differential equation satisfied by the generating function F(x,t). Also, we study the expansion of a function in terms of these polynomials in both real and complex domains and give some conditions under which such an expansion converges.

Recommended Citation

Luong, Son N., "A study of polynomials associated with some generating functions. " Master's Thesis, University of Tennessee, 1989.
https://trace.tennessee.edu/utk_gradthes/13007