Taiwanese Journal of Mathematics

APOSTOL-EULER POLYNOMIALS OF HIGHER ORDER AND GAUSSIAN HYPERGEOMETRIC FUNCTIONS

Qiu-Ming Luo

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Abstract

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 cases and applications that lead to the corresponding formulas of the classical Euler numbers and polynomials of higher order.

Article information

Source
Taiwanese J. Math., Volume 10, Number 4 (2006), 917-925.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500403883

Digital Object Identifier
doi:10.11650/twjm/1500403883

Mathematical Reviews number (MathSciNet)
MR2229631

Zentralblatt MATH identifier
1189.11011

Subjects
Primary: 11B68: Bernoulli and Euler numbers and polynomials 33C05: Classical hypergeometric functions, $_2F_1$ 11B73: Bell and Stirling numbers

Keywords
Euler polynomials Euler polynomials of higher order Apostol-Euler polynomials Apostol-Euler polynomials of higher order Gaussian hypergeometric functions Stirling numbers of the second kind

Citation

Luo, Qiu-Ming. APOSTOL-EULER POLYNOMIALS OF HIGHER ORDER AND GAUSSIAN HYPERGEOMETRIC FUNCTIONS. Taiwanese J. Math. 10 (2006), no. 4, 917--925. doi:10.11650/twjm/1500403883. https://projecteuclid.org/euclid.twjm/1500403883


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References

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