A Simple Generalization of Euler Numbers and Polynomials

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Authors

  • Department of Mathematics, Rowan University, Glassboro, NJ 08028 ,US
  • Department of Mathematics, Rowan University, Glassboro, NJ 08028 ,US

DOI:

https://doi.org/10.18311/jims/2018/20981

Keywords:

Euler Numbers, Euler Polynomials
Quantum Theory

Abstract

In this article, we shall consider a generalization of Euler's numbers and polynomials based on modifying the corresponding generating function. We shall prove some recurrence relations, an explicit formula, and multiplicative properties of the generalized numbers.

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Published

2018-06-01

How to Cite

Hassen, A., & Ernst, C. R. (2018). A Simple Generalization of Euler Numbers and Polynomials. The Journal of the Indian Mathematical Society, 85(3-4), 328–341. https://doi.org/10.18311/jims/2018/20981
Received 2018-04-25
Accepted 2018-04-25
Published 2018-06-01

 

References

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L. J. Mordell, The Sign of the Bernoulli Numbers, The American Mathematical Monthly, Vol. 80, No. 5 (May, 1973), pp. 547-548

H.D. Nguyen and L.C. Cheong, New Convolution Identities for Hypergeometric Bernoulli Polynomials, J. Number Theory 137 (2014), pp. 201-221.

D. C. Vella. Explicit Formula for Bernoulli and Euler Numbers, Integers: Electronic Journal of Combinatorial Number Theory, Vol. 8(1) (2008), #A01

K. J. Wu, Z. W. Sun and H. Pan, Some identities for Bernoulli and Euler polynomials, Fibonacci Quart. 42 (2004), pp. 295- 299.