A Unification of the Generalized Multiparameter Apostol-type Bernoulli, Euler, Fubini, and Genocchi Polynomials of Higher Order
نویسندگان
چکیده
منابع مشابه
Fourier expansions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials
We find Fourier expansions of Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. We give a very simple proof of them.
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The main object of this paper is to introduce and investigate two new classes of generalized Apostol-Euler and Apostol-Genocchi polynomials. In particular, we obtain a new addition formula for the new class of the generalized Apostol-Euler polynomials. We also give an extension and some analogues of the Srivastava-Pintér addition theorem obtained in the works by Srivastava and Pintér 2004 and R...
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The main object of this paper is to investigate the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials. We first establish two relationships between the generalized Apostol-Bernoulli and Apostol-Euler polynomials. It can be found that many results obtained before are special cases of these two relationships. Moreover, we have a study on the sums of products of the Apostol-Bernoulli...
متن کاملAsymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials
We analyze the asymptotic behavior of the Apostol-Bernoulli polynomials Bn(x;λ) in detail. The starting point is their Fourier series on [0, 1] which, it is shown, remains valid as an asymptotic expansion over compact subsets of the complex plane. This is used to determine explicit estimates on the constants in the approximation, and also to analyze oscillatory phenomena which arise in certain ...
متن کاملApostol-euler Polynomials of Higher Order and Gaussian Hypergeometric Functions
The purpose of this paper is to give analogous definitions of Apostol type (see T. M. Apostol [Pacific J. Math. 1 (1951), 161-167]) for the so-called Apostol-Euler numbers and polynomials of higher order. We establish their elementary properties, obtain several explicit formulas involving the Gaussian hypergeometric function and the Stirling numbers of the second kind, and deduce their special ...
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ژورنال
عنوان ژورنال: European Journal of Pure and Applied Mathematics
سال: 2020
ISSN: 1307-5543
DOI: 10.29020/nybg.ejpam.v13i3.3757