Corpus ID: 119654203

Recurrence relations for Apostol-Bernoulli , -Euler and -Genocchi polynomials of higher order

```@article{Prevost2017RecurrenceRF,
title={Recurrence relations for Apostol-Bernoulli , -Euler and -Genocchi polynomials of higher order},
author={Marc Pr'evost},
journal={arXiv: Number Theory},
year={2017}
}```
• Marc Pr'evost
• Published 15 September 2017
• Mathematics
• arXiv: Number Theory
In \cite{luo2006,luosri2005}, Luo and Srivastava introduced some generalizations of the Apostol -Bernoulli polynomials and the Apostol-Euler polynomials. The main object of this paper is to extend the result of \cite{prevost2010} to these generalized polynomials. More precisely, using the Pad\'{e} approximation of the exponential function, we obtain recurrence relations for Apostol-Bernoulli, Euler and also Genocchi polynomials of higher order. As an application we prove lacunary relation for… Expand

References

SHOWING 1-10 OF 26 REFERENCES
Some relationships between the Apostol-Bernoulli and Apostol-Euler polynomials
• Mathematics, Computer Science
• Comput. Math. Appl.
• 2006
The main object of the present sequel to these earlier works is to derive several general properties and relationships involving the apostol-Bernoulli and Apostol-Euler polynomials. Expand
Some generalizations of the Apostol–Bernoulli and Apostol–Euler polynomials
• Mathematics
• 2005
Abstract The main object of this paper is to give analogous definitions of Apostol type (see [T.M. Apostol, On the Lerch Zeta function, Pacific J. Math. 1 (1951) 161–167] and [H.M. Srivastava, SomeExpand
The multiplication formulas for the Apostol–Bernoulli and Apostol–Euler polynomials of higher order
This article obtains the multiplication formulas for the Apostol–Bernoulli and Apostol–Euler polynomials of higher order and deduces some explicit recursive formulas. The λ-multiple power sum andExpand
Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind
• Mathematics, Computer Science
• Appl. Math. Comput.
• 2011
This paper investigates an analogous generalization of the Genocchi polynomials of higher order, that is, the so-called Apostol–Genocchi hailing from the family of the Apostol type polynomes, and derives some basic properties and formulas and considers some interesting applications to the family. Expand
Padé approximation and Apostol-Bernoulli and Apostol-Euler polynomials
• M. Prévost
• Computer Science, Mathematics
• J. Comput. Appl. Math.
• 2010
Using the Pade approximation of the exponential function, recurrence relations between apostol-Bernoulli and between Apostol-Euler polynomials are obtained and some new lacunary recurrence relationships are derived. Expand
APOSTOL-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 higherExpand
Some relationships between the generalized Apostol–Bernoulli polynomials and Hurwitz–Lerch Zeta functions
• Mathematics
• 2006
The main object of this paper is to further investigate the generalized Apostol–Bernoulli polynomials of higher order, which were introduced and studied recently by Luo and Srivastava [2005, JournalExpand
Fourier expansions and integral representations for the Apostol-Bernoulli and Apostol-Euler polynomials
F Fourier expansions for the Apostol-Bernoulli and Apostoli-Euler polynomials are investigated using the Lipschitz summation formula and their integral representations are derived. Expand
Some q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n, and the multiple Hurwitz zeta function
• Mathematics, Computer Science
• Appl. Math. Comput.
• 2008
This paper introduces and investigates some q -extensions of the multiple Hurwitz–Lerch Zeta function Φ n, the Apostol–Bernoulli polynomials B k ( n ) ( x ; λ ) of order n , and the apostol–Euler polynmials E k(n) ( x; λ) ofOrder n . Expand
On the Irrationality of ∑tnAαn+Bβn
Abstract In Andre-Jeannin's article ( C.R. Acad. Sci. Paris Ser. I. 308 (19), 539–541), he proved the irrationality of f ( x )≔∑  x n / w n , where x is an integer in the disk of convergence of theExpand