Integral representations and new generating functions of Chebyshev polynomials

Year 2015, Volume: 44 Issue: 3, 535 - 546, 01.06.2015

Clemente Cesarano

Abstract

In this paper we use the two-variable Hermite polynomials and their

operational rules to derive integral representations of Chebyshev polynomials.

The concepts and the formalism of the Hermite polynomials

Hn(x; y) are a powerful tool to obtain most of the properties of the

Chebyshev polynomials. By using these results, we also show how it is

possible to introduce relevant generalizations of these classes of polynomials

and we derive for them new identities and integral representations.

In particular we state new generating functions for the first and

second kind Chebyshev polynomials.

Keywords

cone normed type spaces, common fixed point, weakly compatible mappings

References

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