Some formulas for the generalized Apostol-type polynomials and numbers

Volume 9, Issue 5, pp 2511--2519 http://dx.doi.org/10.22436/jnsa.009.05.49

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Authors

Wen-Kai Shao - Department of Mathematical Teaching and Research, Yibin Vocational & Technical College, 644003 Yibin, Sichuan, People's Republic of China. Yuan He - Faculty of Science, Kunming University of Science and Technology, 650500 Kunming, Yunnan, People's Republic of China.

Abstract

In this paper, we perform a further investigation for the unified family of the generalized Apostol-Bernoulli, Euler and Genocchi polynomials and numbers introduced by El-Desouky and Gomaa (2014). By using the generating function methods and summation transform techniques, we establish some new formulas for this family of polynomials and numbers, and give some illustrative special cases.

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Keywords

• Apostol-Bernoulli polynomials and numbers
• Apostol-Euler polynomials and numbers
• Apostol-Genocchi polynomials and numbers
• combinatorial identities.

MSC

•  11B68
•  05A19

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