A FEW IDENTITIES AND INTEGRALS INVOLVING POCHHAMMER SYMBOLS, JACOBI POLYNOMIALS, AND THE HYPERGEOMETRIC FUNCTION.

A FEW IDENTITIES AND INTEGRALS INVOLVING POCHHAMMER SYMBOLS, JACOBI POLYNOMIALS, AND THE HYPERGEOMETRIC FUNCTION. | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 17 December 2025 V1 Latest version Share on A FEW IDENTITIES AND INTEGRALS INVOLVING POCHHAMMER SYMBOLS, JACOBI POLYNOMIALS, AND THE HYPERGEOMETRIC FUNCTION. Author : Paweł Szabłowski 0000-0002-3013-5163 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176595675.54305754/v1 144 views 102 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract We expand a hypergeometric function in an orthogonal series of Jacobi polynomials. We first identify identities involving the Pochhammer symbol (rising factorial). We utilize them to discover closed forms for certain integrals of Jacobi polynomials that are multiplied by a hypergeometric function and a Beta density. We can also obtain closed forms for particular series that consist of rising factorials, which generalize binomial series, by using well-known properties of the hypergeometric function. We can also get some simplifying identities of generalized hypergeometric functions. Supplementary Material File (pracahypmod.pdf) Download 161.09 KB Information & Authors Information Version history V1 Version 1 17 December 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords beta distribution hypergeometric function jacobi polynomials pochhammer symbol Authors Affiliations Paweł Szabłowski 0000-0002-3013-5163 [email protected] Politechnika Warszawska View all articles by this author Metrics & Citations Metrics Article Usage 144 views 102 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Paweł Szabłowski. A FEW IDENTITIES AND INTEGRALS INVOLVING POCHHAMMER SYMBOLS, JACOBI POLYNOMIALS, AND THE HYPERGEOMETRIC FUNCTION.. Authorea . 17 December 2025. DOI: https://doi.org/10.22541/au.176595675.54305754/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. 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