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New Clebsch–Gordan‐type integrals involving threefold products of complete elliptic integrals.
- Source :
-
Mathematical Methods in the Applied Sciences . Nov2023, Vol. 46 Issue 17, p17773-17787. 15p. - Publication Year :
- 2023
-
Abstract
- Multiple elliptic integrals related to the generalized Clebsch–Gordan (CG) integral are of importance in many areas in physics and special functions theory. Zhou has introduced and applied Legendre function‐based techniques to prove symbolic evaluations for integrals of CG form involving twofold and threefold products of complete elliptic integral expressions, and this includes Zhou's remarkable proof of an open problem due to Wan. The foregoing considerations motivate the results introduced in this article, in which we prove closed‐form evaluations for new CG‐type integrals that involve threefold products of the complete elliptic integrals K$$ \mathbf{K} $$ and E$$ \mathbf{E} $$. Our methods are based on the use of fractional derivative operators, via a variant of a technique we had previously referred to as semi‐integration by parts. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ELLIPTIC integrals
*INTEGRALS
*GENERALIZED integrals
*SPECIAL functions
Subjects
Details
- Language :
- English
- ISSN :
- 01704214
- Volume :
- 46
- Issue :
- 17
- Database :
- Academic Search Index
- Journal :
- Mathematical Methods in the Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 173586018
- Full Text :
- https://doi.org/10.1002/mma.9530