On Some Arithmetical Properties of the Genocchi Numbers and Polynomials
<p/> <p>We investigate the properties of the Genocchi functions and the Genocchi polynomials. We obtain the Fourier transform on the Genocchi function. We have the generating function of <inline-formula> <graphic file="1687-1847-2008-195049-i1.gif"/></inline-form...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2008-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://www.advancesindifferenceequations.com/content/2008/195049 |
| Summary: | <p/> <p>We investigate the properties of the Genocchi functions and the Genocchi polynomials. We obtain the Fourier transform on the Genocchi function. We have the generating function of <inline-formula> <graphic file="1687-1847-2008-195049-i1.gif"/></inline-formula>-Genocchi polynomials. We define the Cangul-Ozden-Simsek's type twisted <inline-formula> <graphic file="1687-1847-2008-195049-i2.gif"/></inline-formula>-Genocchi polynomials and numbers. We also have the generalized twisted <inline-formula> <graphic file="1687-1847-2008-195049-i3.gif"/></inline-formula>-Genocchi numbers attached to the Dirichlet's character <inline-formula> <graphic file="1687-1847-2008-195049-i4.gif"/></inline-formula>. Finally, we define zeta functions related to <inline-formula> <graphic file="1687-1847-2008-195049-i5.gif"/></inline-formula>-Genocchi polynomials and have the generating function of the generalized <inline-formula> <graphic file="1687-1847-2008-195049-i6.gif"/></inline-formula>-Genocchi numbers attached to <inline-formula> <graphic file="1687-1847-2008-195049-i7.gif"/></inline-formula>.</p> |
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| ISSN: | 1687-1839 1687-1847 |