Document Type : Original Article

Authors

• Soodeh Mehboodi ¹
• Mohammad Hadi Hooshmand ²

¹ Zand Institute of Higher Education, Shiraz, Iran.

² Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran.

Abstract

Analytic summability of functions was introduced by Hooshmand in 2016. He used Bernoulli numbers and polynomials B_n(z) to define analytic summability and related analytic summand functions. Since the Bernoulli and Euler polynomials have many similarities, so it motivated us to define differenceability and introduce analytic difference function of a complex or real function by utilizing the Euler numbers and polynomials E_n(z). Also, we prove some criteria for analytic differenceability of analytic functions. Moreover, we observe that the analytic difference function is indeed a series of the Euler polynomials and arrive at some series convergence tests for Euler polynomial series Σ^∞_n=0c_nE_n(z).

Keywords

• Bernoulli and Euler polynomials
• Bernoulli and Euler numbers
• Analytic summability