Moments of Ramanujan's generalized elliptic integrals and extensions of Catalan's constant (Q719586): Difference between revisions

The authors deal with the moments of Ramanujan's alternative elliptic integrals and of related hypergeometric functions. There are obtained closed forms of Catalan-related constants and various new hypergeometric identities.

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reviewed by

Cristinel Mortici

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zbMATH Keywords

elliptic integrals

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hypergeometric functions

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moments

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Catalan's constant

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MaRDI profile type

Publication

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full work available at URL

https://doi.org/10.1016/j.jmaa.2011.06.001

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cites work

A certain series associated with Catalan's constant

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Generalized elliptic integrals and modular equations

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Q4222737

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The Computation of Previously Inaccessible Digits of $pi^2$ and Catalan’s Constant

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Ramanujan's Theories of Elliptic Functions to Alternative Bases

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Ramanujan's Series for 1/π: A Survey

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Q3476890

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Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi

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A Cubic Counterpart of Jacobi's Identity and the AGM

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A class of series acceleration formulae for Catalan's constant

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Generalized elliptic integrals

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Q5518575

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Q5508372

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Ramanujan-type formulae for $1/\pi$: A second wind?

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Identifiers

zbMATH Open document ID

1228.11183

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Mathematics Subject Classification ID

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10.1016/J.JMAA.2011.06.001

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Sitelinks

Mathematics(1 entry)

mardi Publication:719586

@@ description / en / description / en @@
-scientific article
+scientific article; zbMATH DE number 5956108
@@ Property / DOI @@
-.1016/j.jmaa.2011.06.001
@@ Property / DOI: 10.1016/j.jmaa.2011.06.001 / rank @@
-Normal rank
@@ Property / full work available at URL @@
+https://doi.org/10.1016/j.jmaa.2011.06.001
+Normal rank
@@ Property / OpenAlex ID @@
+W2010567827
@@ Property / OpenAlex ID: W2010567827 / rank @@
+Normal rank
@@ Property / cites work @@
+A certain series associated with Catalan's constant
+Normal rank
@@ Property / cites work @@
+Generalized elliptic integrals and modular equations
+Normal rank
@@ Property / cites work @@
+Q4222737
@@ Property / cites work: Q4222737 / rank @@
+Normal rank
@@ Property / cites work @@
+The Computation of Previously Inaccessible Digits of $pi^2$ and Catalan’s Constant
+Normal rank
@@ Property / cites work @@
+Ramanujan's Theories of Elliptic Functions to Alternative Bases
+Normal rank
@@ Property / cites work @@
+Ramanujan's Series for 1/π: A Survey
@@ Property / cites work: Ramanujan's Series for 1/π: A Survey / rank @@
+Normal rank
@@ Property / cites work @@
+Q3476890
@@ Property / cites work: Q3476890 / rank @@
+Normal rank
@@ Property / cites work @@
+Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi
+Normal rank
@@ Property / cites work @@
+A Cubic Counterpart of Jacobi's Identity and the AGM
+Normal rank
@@ Property / cites work @@
+A class of series acceleration formulae for Catalan's constant
+Normal rank
@@ Property / cites work @@
+Generalized elliptic integrals
@@ Property / cites work: Generalized elliptic integrals / rank @@
+Normal rank
@@ Property / cites work @@
+Q5518575
@@ Property / cites work: Q5518575 / rank @@
+Normal rank
@@ Property / cites work @@
+Q5508372
@@ Property / cites work: Q5508372 / rank @@
+Normal rank
@@ Property / cites work @@
+Ramanujan-type formulae for $1/\pi$: A second wind?
+Normal rank
@@ Property / DOI @@
+.1016/J.JMAA.2011.06.001
@@ Property / DOI: 10.1016/J.JMAA.2011.06.001 / rank @@
+Normal rank