Poly-Euler polynomials and Arakawa-Kaneko type zeta functions (Q466147)
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scientific article; zbMATH DE number 6361347
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Poly-Euler polynomials and Arakawa-Kaneko type zeta functions |
scientific article; zbMATH DE number 6361347 |
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Poly-Euler polynomials and Arakawa-Kaneko type zeta functions (English)
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24 October 2014
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polylogarithms
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Euler polynomials
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Arakawa-Kaneko zeta functions
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Poly-Euler polynomials \(E_n^{(k)}(x)\) are defined via the generating function NEWLINE\[NEWLINE \frac{2\text{Li}_k(1-e^{-t})}{t(e^t+1)}e^{xt}=\sum_{n=0}^\infty E_n^{(k)}(x)\frac{t^n}{n!} NEWLINE\]NEWLINE where \(\text{Li}_k(x)=\sum_{m=1}^\infty \frac{x^m}{m^k}\). The author proves some identities for these polynomials and studies their relations to some versions of zeta- and \(L\)-functions.
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