Abstract
The main purpose of this paper is to present new -extensions of Apostol's type Euler polynomials using the fermionic -adic integral on . We define the - -Euler polynomials and obtain the interpolation functions and the Hurwitz type zeta functions of these polynomials. We define -extensions of Apostol type's Euler polynomials of higher order using the multivariate fermionic -adic integral on . We have the interpolation functions of these - -Euler polynomials. We also give -extensions of Apostol's type Euler polynomials of higher order and have the multiple Hurwitz type zeta functions of these - -Euler polynomials.
Highlights
Many authors have studied on various kinds of q-analogues of the Euler numbers and polynomials cf., 1–39 .T Kim 7–23 has published remarkable research results for q-extensions of the Euler numbers and polynomials and their interpolation functions
In 13, T Kim presented a systematic study of some families of multiple q-Euler numbers and polynomials
In 20, Kim studied some families of multiple q-Genocchi and q-Euler numbers using the multivariate p-adic q-Volkenborn integral on Zp, and gave interesting identities related to these numbers
Summary
The main purpose of this paper is to present new q-extensions of Apostol’s type Euler polynomials using the fermionic p-adic integral on Zp. We define the q-λ-Euler polynomials and obtain the interpolation functions and the Hurwitz type zeta functions of these polynomials. We define qextensions of Apostol type’s Euler polynomials of higher order using the multivariate fermionic p-adic integral on Zp. We have the interpolation functions of these q-λ-Euler polynomials. Q -extensions of Apostol’s type Euler polynomials of higher order and have the multiple Hurwitz type zeta functions of these h, q -λ-Euler polynomials. In 20 , Kim studied some families of multiple q-Genocchi and q-Euler numbers using the multivariate p-adic q-Volkenborn integral on Zp, and gave interesting identities related to these numbers. Kim 21 studied some families of q-Euler numbers and polynomials of Nolund’s type using multivariate fermionic p-adic integral on Zp
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