Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions

In the paper, by virtue of the binomial inversion formula, a general formula of higher order derivatives for a ratio of two differentiable function, and other techniques, the authors compute several sums in terms of the beta function and its partial derivatives, polygamma functions, the Gauss hyperg...

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Detalles Bibliográficos
Autores principales: Qi, Feng, Huang, Chuan-Jun
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2020
Materias:
Original Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7444454/
https://www.ncbi.nlm.nih.gov/pubmed/32863811
http://dx.doi.org/10.1007/s13398-020-00927-y
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author Qi, Feng
Huang, Chuan-Jun
author_facet Qi, Feng
Huang, Chuan-Jun
author_sort Qi, Feng
collection PubMed
description In the paper, by virtue of the binomial inversion formula, a general formula of higher order derivatives for a ratio of two differentiable function, and other techniques, the authors compute several sums in terms of the beta function and its partial derivatives, polygamma functions, the Gauss hypergeometric function, and a determinant. These results generalize known ones in combinatorics.
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spelling pubmed-74444542020-08-26 Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions Qi, Feng Huang, Chuan-Jun Rev R Acad Cienc Exactas Fis Nat A Mat Original Paper In the paper, by virtue of the binomial inversion formula, a general formula of higher order derivatives for a ratio of two differentiable function, and other techniques, the authors compute several sums in terms of the beta function and its partial derivatives, polygamma functions, the Gauss hypergeometric function, and a determinant. These results generalize known ones in combinatorics. Springer International Publishing 2020-08-24 2020 /pmc/articles/PMC7444454/ /pubmed/32863811 http://dx.doi.org/10.1007/s13398-020-00927-y Text en © The Royal Academy of Sciences, Madrid 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Original Paper
Qi, Feng
Huang, Chuan-Jun
Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions
title Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions
title_full Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions
title_fullStr Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions
title_full_unstemmed Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions
title_short Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions
title_sort computing sums in terms of beta, polygamma, and gauss hypergeometric functions
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7444454/
https://www.ncbi.nlm.nih.gov/pubmed/32863811
http://dx.doi.org/10.1007/s13398-020-00927-y
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