Extensions of the Genocchi polynomials and their Fourier expansions and integral representations

By Qiu-Ming Luo. 2011

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We extend the Genocchi polynomials and investigate their Fourier expansions and integral representations. We obtain their formulas at rational arguments in terms of Hurwitz zeta function and show an explicit relationship with Gaussian hypergeometric functions. Some known results for the classical Genocchi polynomials are also deduced.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/b75365e66baf7cb96850ced457f77cb6ba5575e9