On extended Carlitz’'s type q-Euler numbers and polynomials
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We give a new sequence of extended Carlitz's type q-Euler numbers and polynomials. We have identities for these q-Euler numbers and polynomials and a distribution relation for new q-Euler polynomial using fermionic p-adic q-integral on Zp. We also consider generalized extended Carlitz's type q-Euler polynomials and numbers attached to the Dirichlet's character Â. Finally, we study q-zeta function which interpolates extended Carlitz's type q-Euler polynomials at negative integers.
Abstract
We give a new sequence of extended Carlitz's type q-Euler numbers and polynomials. We have identities for these q-Euler numbers and polynomials and a distribution relation for new q-Euler polynomial using fermionic p-adic q-integral on Zp. We also consider generalized extended Carlitz's type q-Euler polynomials and numbers attached to the Dirichlet's character Â. Finally, we study q-zeta function which interpolates extended Carlitz's type q-Euler polynomials at negative integers.
참고문헌 (9)
- L. Carlitz, "q-Bernoulli numbers and polynomials", Duke Mathematical Journal, 15, pp.987~1000 (1948)
- L. Carlitz, "q-Bernoulli and Eulerian numbers", Transactions of the American Mathematical Society, 76, pp.332~350 (1954)
- L. Carlitz, "Expansion of q-Bernoulli numbers", Duke Mathematical Journal, 25, pp.355~364 (1958)
- T. Kim, "Some identities on the q-Euler polynomials of higher order and q-Stirling numbers by the fermionic p-adic integral on Zp", Russian Journal of Mathematical Physics, 16, pp.484~491 (2009)
- T. Kim, "Note on the Euler q-zeta functions", Journal of Number Theory, 129, pp.1798~1804 (2009)
- T. Kim, "Barnes-type multiple q-zeta functions and q-Euler polynomials", J. Phys. A : Math. Theor., 43, pp.11~ (2010)
- T. Kim, "q-Volkenborn integration", Russian Journal of Mathematical Physics, 9, pp.288~299 (2002)
- T. Kim, "New approach to q-Euler numbers and polynomials", Advances in Difference Equations 2010, pp.9~ (2010)
- 김태균, "NOTE ON CARLITZ’S TYPE q-EULER NUMBERS AND POLYNOMIALS", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 13(2), pp.149~155 (2010), 장전수학회