In this paper we provide some relationships between Catalan’s constant and the 3F2 and 4F3 hypergeometric functions, deriving them from some parametric integrals. In particular, using the complete elliptic integral of the first kind, we found an alternative proof of a result of Ramanujan for 3F2, a second identity related to 4F3 and using the complete elliptic integral of the second kind we obtain an identity by Adamchik.

Identities for Catalan’s constant arising from integrals depending on a parameter / Ferretti, F.; Gambini, A.; Ritelli, D.. - In: ACTA MATHEMATICA SINICA. - ISSN 1439-8516. - 36:10(2020), pp. 1083-1093. [10.1007/s10114-020-9451-9]

Identities for Catalan’s constant arising from integrals depending on a parameter

Gambini A.
;
2020

Abstract

In this paper we provide some relationships between Catalan’s constant and the 3F2 and 4F3 hypergeometric functions, deriving them from some parametric integrals. In particular, using the complete elliptic integral of the first kind, we found an alternative proof of a result of Ramanujan for 3F2, a second identity related to 4F3 and using the complete elliptic integral of the second kind we obtain an identity by Adamchik.
2020
33C20; 33C75; Catalan constant; elliptic integral; hypergeometric functions
01 Pubblicazione su rivista::01a Articolo in rivista
Identities for Catalan’s constant arising from integrals depending on a parameter / Ferretti, F.; Gambini, A.; Ritelli, D.. - In: ACTA MATHEMATICA SINICA. - ISSN 1439-8516. - 36:10(2020), pp. 1083-1093. [10.1007/s10114-020-9451-9]
File allegati a questo prodotto
File Dimensione Formato  
Ferretti_Identities-for-Catalan-postprint_2020.pdf

accesso aperto

Tipologia: Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 302.19 kB
Formato Adobe PDF
302.19 kB Adobe PDF
Ferretti_Identities-for-Catalan_2020.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 194.29 kB
Formato Adobe PDF
194.29 kB Adobe PDF   Contatta l'autore

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1468734
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 4
social impact