Some expansions of functions based upon two sequences of hypergeometric polynomials

Abstract

In this paper, we introduce two series expansions whose basis functions are two sequences of hypergeometric polynomials. We then present a systematic and detailed study of the general properties of each of these series expansions. We consider several illustrative examples to show the computational efficiency of our expansions in comparison to the usual Taylor series expansion. We also discuss some expansions of mixed types which are related to the results and assertions presented in this paper.

Mathematics Subject Classification (2010):

• Primary: 30B10, 30B50, 41A58
• Secondary: 33C45

Key words:

• Expansion of functions
• hypergeometric polynomials
• linear functionals
• interpolation problems with unlimited conditions
• Taylor series expansions
• Fourier trigonometric series
• generating functions