The Journal of the Indian Mathematical Society

A Simple Generalization of Euler Numbers and Polynomials


Affiliations

  • Rowan University, Department of Mathematics, Glassboro, NJ, 08028, United States

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.

Keywords

Euler Numbers, Euler Polynomials

Subject Discipline

Mathematical Sciences

Full Text:

References

L. Carlitz and R. Scoville, The Sign of the Bernoulli and Euler Numbers, The American Mathematical Monthly, Vol. 80, No. 5 (May, 1973), pp. 548-549

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.


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