<inline-formula> <graphic file="1687-1847-2008-815750-i1.gif"/></inline-formula>-Genocchi Numbers and Polynomials Associated with <inline-formula> <graphic file="1687-1847-2008-815750-i2.gif"/></inline-formula>-Genocchi-Type <inline-formula> <graphic file="1687-1847-2008-815750-i3.gif"/></inline-formula>-Functions
<p/> <p>The main purpose of this paper is to study on generating functions of the <inline-formula> <graphic file="1687-1847-2008-815750-i4.gif"/></inline-formula>-Genocchi numbers and polynomials. We prove new relation for the generalized <inline-formula>...
| 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/2008/815750 |
| Summary: | <p/> <p>The main purpose of this paper is to study on generating functions of the <inline-formula> <graphic file="1687-1847-2008-815750-i4.gif"/></inline-formula>-Genocchi numbers and polynomials. We prove new relation for the generalized <inline-formula> <graphic file="1687-1847-2008-815750-i5.gif"/></inline-formula>-Genocchi numbers which is related to the <inline-formula> <graphic file="1687-1847-2008-815750-i6.gif"/></inline-formula>-Genocchi numbers and <inline-formula> <graphic file="1687-1847-2008-815750-i7.gif"/></inline-formula>-Bernoulli numbers. By applying Mellin transformation and derivative operator to the generating functions, we define <inline-formula> <graphic file="1687-1847-2008-815750-i8.gif"/></inline-formula>-Genocchi zeta and <inline-formula> <graphic file="1687-1847-2008-815750-i9.gif"/></inline-formula>-functions, which are interpolated <inline-formula> <graphic file="1687-1847-2008-815750-i10.gif"/></inline-formula>-Genocchi numbers and polynomials at negative integers. We also give some applications of generalized <inline-formula> <graphic file="1687-1847-2008-815750-i11.gif"/></inline-formula>-Genocchi numbers.</p> |
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| ISSN: | 1687-1839 1687-1847 |