Explicit Formulas for Some Infinite <sub>3</sub><i>F</i><sub>2</sub>(1)-Series

Explicit Formulas for Some Infinite <sub>3</sub><i>F</i><sub>2</sub>(1)-Series

We establish two recurrence relations for some Clausen’s hypergeometric functions with unit argument. We solve them to give the explicit formulas. Additionally, we use the moments of Ramanujan’s generalized elliptic integrals to obtain these recurrence relations.

Bibliographic Details
Main Author: Kwang-Wu Chen
Format: Article
Language:English
Published: MDPI AG 2021-06-01
Series:Axioms
Subjects:
Clausen’s hypergeometric functions
elliptic integrals
moments
Online Access:https://www.mdpi.com/2075-1680/10/2/125
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spelling doaj-89ffb1dfc44e4457ad34bc71791cb1ce2021-07-01T00:37:06ZengMDPI AGAxioms2075-16802021-06-011012512510.3390/axioms10020125Explicit Formulas for Some Infinite <sub>3</sub><i>F</i><sub>2</sub>(1)-SeriesKwang-Wu Chen0Department of Mathematics, University of Taipei, No. 1, Ai-Guo West Road, Taipei 10048, TaiwanWe establish two recurrence relations for some Clausen’s hypergeometric functions with unit argument. We solve them to give the explicit formulas. Additionally, we use the moments of Ramanujan’s generalized elliptic integrals to obtain these recurrence relations.https://www.mdpi.com/2075-1680/10/2/125Clausen’s hypergeometric functionselliptic integralsmoments
collection DOAJ
language English
format Article
sources DOAJ
author Kwang-Wu Chen
spellingShingle Kwang-Wu Chen
Explicit Formulas for Some Infinite <sub>3</sub><i>F</i><sub>2</sub>(1)-Series
Axioms
Clausen’s hypergeometric functions
elliptic integrals
moments
author_facet Kwang-Wu Chen
author_sort Kwang-Wu Chen
title Explicit Formulas for Some Infinite <sub>3</sub><i>F</i><sub>2</sub>(1)-Series
title_short Explicit Formulas for Some Infinite <sub>3</sub><i>F</i><sub>2</sub>(1)-Series
title_full Explicit Formulas for Some Infinite <sub>3</sub><i>F</i><sub>2</sub>(1)-Series
title_fullStr Explicit Formulas for Some Infinite <sub>3</sub><i>F</i><sub>2</sub>(1)-Series
title_full_unstemmed Explicit Formulas for Some Infinite <sub>3</sub><i>F</i><sub>2</sub>(1)-Series
title_sort explicit formulas for some infinite <sub>3</sub><i>f</i><sub>2</sub>(1)-series
publisher MDPI AG
series Axioms
issn 2075-1680
publishDate 2021-06-01
description We establish two recurrence relations for some Clausen’s hypergeometric functions with unit argument. We solve them to give the explicit formulas. Additionally, we use the moments of Ramanujan’s generalized elliptic integrals to obtain these recurrence relations.
topic Clausen’s hypergeometric functions
elliptic integrals
moments
url https://www.mdpi.com/2075-1680/10/2/125
work_keys_str_mv AT kwangwuchen explicitformulasforsomeinfinitesub3subifisub2sub1series
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