Integral representations and new generating functions of Chebyshev polynomials

Authors : Clemente CESARANO

Pages : 535-546

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Publication Date : 2015-06-01

Article Type : Research Paper

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 Hninsert ignore into journalissuearticles values(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