A note on generalized Euler numbers and polynomials

Abstract

In this paper we construct new generalized Euler polynomials and generalized Euler numbers attached to χ. We investigate some of the properties that are related to generalized Euler polynomials. We also derive the existence of a specific interpolation function that interpolates generalized Euler polynomials at negative integers. Finally, we investigate computationally the roots of the generalized Euler polynomials E _{n, χ}(x) for values of the index n.

Keywords:

• Euler numbers
• Euler polynomials
• Generalized Euler numbers
• Generalized Euler polynomials

Acknowledgements

This work was supported by Hannam University Research Fund, 2007.