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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
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