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Analytic differenceablity of functions | ||
Mathematical Analysis and its Contemporary Applications | ||
دوره 3، شماره 1، بهار 2021، صفحه 1-12 اصل مقاله (354.98 K) | ||
نوع مقاله: Original Article | ||
نویسندگان | ||
Soodeh Mehboodi1؛ Mohammad Hadi Hooshmand ![]() | ||
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 | ||
آمار تعداد مشاهده مقاله: 6 تعداد دریافت فایل اصل مقاله: 2 |