发表机构
Faculty of Civil Engineering, University of Zagreb; School of Applied Mathematics and Informatics, Josip Juraj Strossmayer University of Osijek; Department of Mathematics, Faculty of Science, University of Akdeniz（萨格勒布大学土木工程学院; 约瑟夫·尤拉伊·斯特罗斯梅耶尔应用数学与信息学院; 安塔利亚大学理学院数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究由Frobenius-Euler型多项式生成函数导出的级数族，证明其生成Hurwitz和Lerch zeta函数，给出解析延拓、插值及拉普拉斯变换表示。
AI 中文摘要
本文研究由Frobenius-Euler型和Apostol型多项式及数的生成函数导出的某一级数族。当考察该级数的特殊情形时，表明它能生成一些著名的zeta函数族，如Hurwitz zeta函数和Lerch zeta函数等。我们还为这些关系提出了一个开放问题。我们给出了该函数的解析延拓。利用柯西留数定理，我们证明该级数在负整数处插值Frobenius-Euler型多项式。此外，通过对这些多项式的生成函数应用拉普拉斯变换，我们得到了涉及Lerch zeta函数和这些多项式的无穷级数表示。另外，我们表明该插值函数可以用Lerch zeta函数和Hurwitz zeta函数来表示。文中还给出了结果的一些特殊值。
英文摘要
This paper deals with a certain family of series which is derived from generating functions of the Frobenius-Euler and Apostol type polynomials and numbers. When special cases of this series are examined, it is shown that it generates some well-known families of zeta functions, such as the Hurwitz zeta and the Lerch zeta, etc. We also give an open problem for these relation. We give analytic continuation of this function. By using the Cauchy Residue Theorem, We show that this series interpolates the Frobenius-Euler type polynomials at negative integers. Moreover, by applying the Laplace transform to the generating function for these polynomials, we get infinite series representations involving the Lerch zeta function and these polynomials. In addition, We show that this interpolation function can be representation in terms of the Lerch zeta function and the Hurwitz zeta function. Some special values for the results are also given.
