{"title":"On Sums of Special Functions","authors":"Yu. A. Brychkov","doi":"10.1134/s1995080224602418","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Sums of the form <span>\\(\\sum_{k=0}^{n}\\frac{\\prod_{i=1}^{p}\\left(a_{i}\\right)_{k}}{\\prod_{j=1}^{q}\\left(b_{j}\\right)_{k}}w^{k}{}F_{k}(z)\\)</span> are considered<span>\\(,\\)</span> where <span>\\(F_{k}(z)\\)</span> are special functions of hypergeometric type. Such sums involving Bessel, Struve, incomplete gamma functions, and Laguerre, Hermite, Jacobi, Legendre, and Chebyshev polynomials can be represented in terms of the Kampé de Fériet and generalized Horn hypergeometric functions of two variables.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":"37 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995080224602418","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Sums of the form \(\sum_{k=0}^{n}\frac{\prod_{i=1}^{p}\left(a_{i}\right)_{k}}{\prod_{j=1}^{q}\left(b_{j}\right)_{k}}w^{k}{}F_{k}(z)\) are considered\(,\) where \(F_{k}(z)\) are special functions of hypergeometric type. Such sums involving Bessel, Struve, incomplete gamma functions, and Laguerre, Hermite, Jacobi, Legendre, and Chebyshev polynomials can be represented in terms of the Kampé de Fériet and generalized Horn hypergeometric functions of two variables.
AbstractSums of the form （(\sum_{k=0}^{n}\frac{prod_{i=1}^{p}\left(a_{i}\right)_{k}}{prod_{j=1}^{q}\left(b_{j}\right)_{k}}w^{k}{}F_{k}(z)\）被认为是（、\其中 \(F_{k}(z)\) 是超几何类型的特殊函数。涉及贝塞尔函数、斯特鲁夫函数、不完全伽马函数、拉盖尔多项式、赫米特多项式、雅可比多项式、勒让德多项式和切比雪夫多项式的这类和可以用两个变量的坎佩-德-费里特函数和广义霍恩超几何函数来表示。
期刊介绍：
Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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