q-Euler and Genocchi numbers

Details q-Euler and Genocchi numbers q-Euler and Genocchi numbers

2005-06-14

arxiv.org/abs/math/0506278v1

Mathematics

Number Theory

7 pages

Scientific paper

Carlitz has introduced an interesting $q$-analogue of Frobenius-Euler numbers in [4]. He has indicated a corresponding Stadudt-Clausen theorem and also some interesting congruence properties of the $q$-Euler numbers. In this paper we give another construction of $q$-Euler numbers, which are different than his $q$-Euler numbers. By using our $q$-Euler numbers, we define the $q$-analogue of Genocchi numbers and investigate the relations between $q$-Euler numbers and $q$-analogs of Genocchi numbers.

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