Analytic differenceablity of functions

Mathematical Analysis and its Contemporary Applications

دوره 3، شماره 1، بهار 2021، صفحه 1-12  

نوع مقاله: Original Article

نویسندگان

Soodeh Mehboodi¹؛ Mohammad Hadi Hooshmand ²

¹Zand Institute of Higher Education, Shiraz, Iran.

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

چکیده

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 differenceablity 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 differenceablity 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 $\sum_{n=0}^{\infty}c_nE_n(z)$.

کلیدواژه‌ها

Bernoulli and Euler polynomials؛ Bernoulli and Euler numbers؛ Analytic summability