Abstract
In this paper, we study some properties of the generalized Apostol-type polynomials (see (Luo and Srivastava in Appl. Math. Comput. 217:5702-5728, 2011)), including the recurrence relations, the differential equations and some other connected problems, which extend some known results. We also deduce some properties of the generalized Apostol-Euler polynomials, the generalized Apostol-Bernoulli polynomials, and Apostol-Genocchi polynomials of high order.MSC:11B68, 33C65.
Highlights
In this paper, we study some properties of the generalized Apostol-type polynomials
Definition . (Luo and Srivastava [ ]) The generalized Apostol type polynomials Fn(α)(x; λ; u, v) (α ∈ N, λ, u, v ∈ C) of order α are defined by means of the following generating function:
We study some other properties of the generalized Apostol type polynomials Fn(α)(x; λ; u, v), including the recurrence relations, the differential equations and some connection problems, which extend some known results
Summary
We study some properties of the generalized Apostol-type polynomials (Apostol [ ]; see Srivastava [ ]) The Apostol-Bernoulli polynomials Bn(x; λ) (λ ∈ C) are defined by means of the following generating function: zexz λez – = (Luo and Srivastava [ ]) The Apostol-Bernoulli polynomials Bn(α)(x; λ) (λ ∈ C) of order α ∈ N are defined by means of the following generating function: z λez –
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