# zbMATH — the first resource for mathematics

Interpolation functions of $$q$$-extensions of Apostol’s type Euler polynomials. (English) Zbl 1176.41004
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 $$\mathbb Z_p$$. We define the $$q-\lambda$$-Euler polynomials and obtain the interpolation functions and the Hurwitz type zeta functions of these polynomials. We define $$q$$-extensions of Apostol type’s Euler polynomials of higher order using the multivariate fermionic $$p$$-adic integral on $$\mathbb Z_p$$. We have the interpolation functions of these $$q-\lambda$$-Euler polynomials. We also give $$(h,q)$$-extensions of Apostol’s type Euler polynomials of higher order and have the multiple Hurwitz type zeta functions of these $$(h,q)-\lambda$$-Euler polynomials.

##### MSC:
 41A05 Interpolation in approximation theory 11B68 Bernoulli and Euler numbers and polynomials 11M35 Hurwitz and Lerch zeta functions
Full Text: