A note on the \(q\)-Genocchi numbers and polynomials with weak weight \(\alpha\) (Q2908283)
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scientific article; zbMATH DE number 6076711
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on the \(q\)-Genocchi numbers and polynomials with weak weight \(\alpha\) |
scientific article; zbMATH DE number 6076711 |
Statements
4 September 2012
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p-adic fermionic q-Volkenborn integral
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Volkenborn integral
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\(q\)-Genocchi polynomials and numbers with weak weight
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zeta functions
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A note on the \(q\)-Genocchi numbers and polynomials with weak weight \(\alpha\) (English)
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Using the \(p\)-adic fermionic \(q\)-Volkenborn integral, the authors give many identities and relations for \(q\)-Genocchi polynomials and numbers with weak weight \(\alpha\). By applying a derivative operator to generating functions for the \(q\)-Genocchi polynomials and numbers with weak weight \(\alpha\), the authors define \(q\)-zeta functions, which interpolate the \(q\)-Genocchi polynomials and numbers with weak weight \(\alpha\) at negative integers.
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