Analytic differenceability of functions

Mathematical Analysis and its Contemporary Applications

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

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30495/maca.2021.680048

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 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).

کلیدواژه‌ها

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