New approach to q-Euler, Genocchi numbers and their interpolation functions
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In [1], Cangul-Ozden-Simsek constructed a q-Genocchi numbers of higher order and gave Witt’s formula of these numbers by using a p-adic fermionic integral on Zp. In this paper, we give another constructions of a q-Euler and Genocchi numbers of higher order, which are different than their q-Genocchi and Euler numbers of higher order. By using our q-Euler and Genocchi numbers of higher order, we can investigate the interesting relationship between w-q-Euler numbers and w-q-Genocchi numbers. Finally, we give the interpolation functions of these numbers . This paper’s online version is arXiv:0901.0353.
Abstract
In [1], Cangul-Ozden-Simsek constructed a q-Genocchi numbers of higher order and gave Witt’s formula of these numbers by using a p-adic fermionic integral on Zp. In this paper, we give another constructions of a q-Euler and Genocchi numbers of higher order, which are different than their q-Genocchi and Euler numbers of higher order. By using our q-Euler and Genocchi numbers of higher order, we can investigate the interesting relationship between w-q-Euler numbers and w-q-Genocchi numbers. Finally, we give the interpolation functions of these numbers . This paper’s online version is arXiv:0901.0353.
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