2021/03/16 by Qian Tang, Tang Qian, Qian, Tang
Mathematics · #Advanced Mathematical Identities #Mathematical functions and polynomials #Mathematics and Applications #math.CA #msc:05A40 #msc:33Exx #msc:40A25
paper · pdf · doi:10.48550/arxiv.2103.09117
arxiv created 2021/03/16 · arxiv updated 2021/03/17
We will use analytic function theory and Fourier analysis to establish a characterization for some classical umbral calculus, which will focus on the generalization of the evaluation function. Although we cannot cover all the umbral calculus people care about, the part about Bernoulli numbers can still answer an open question about fractional sums raised by Müller and Schleicher in 2005 and synthesize some common analysis results. We will only develop the results which are sufficient to serve the purpose of this article, but at the same time, we will briefly mention some possible extensions.