Matches in SemOpenAlex for { <https://semopenalex.org/work/W2762156722> ?p ?o ?g. }
Showing items 1 to 86 of
86
with 100 items per page.
- W2762156722 abstract "Motivated by our previous work on hypergeometric functions and the parbelos constant, we perform a deeper investigation on the interplay among generalized complete elliptic integrals, Fourier-Legendre (FL) series expansions, and ${}_p F_q$ series. We produce new hypergeometric transformations and closed-form evaluations for new series involving harmonic numbers, through the use of the integration method outlined as follows: Letting $K$ denote the complete elliptic integral of the first kind, for a suitable function $g$ we evaluate integrals such as $$ int_{0}^{1} Kleft( sqrt{x} right) g(x) , dx $$ in two different ways: (1) by expanding $K$ as a Maclaurin series, perhaps after a transformation or a change of variable, and then integrating term-by-term; and (2) by expanding $g$ as a shifted FL series, and then integrating term-by-term. Equating the expressions produced by these two approaches often gives us new closed-form evaluations, as in the formulas involving Catalan's constant $G$ $$ sum _{n = 0}^{infty } binom{2 n}{n}^2 frac{H_{n + frac{1}{4}} - H_{n-frac{1}{4}}}{16^{n} } = frac{Gamma^4 left(frac{1}{4}right)}{8 pi^2}-frac{4 G}{pi},$$ $$ sum _{m, n geq 0} frac{binom{2 m}{m}^2 binom{2 n}{n}^2 }{ 16^{m + n} (m+n+1) (2 m+3) } = frac{7 zeta (3) - 4 G}{pi^2}.$$" @default.
- W2762156722 created "2017-10-20" @default.
- W2762156722 creator A5000663767 @default.
- W2762156722 creator A5066938892 @default.
- W2762156722 creator A5078146626 @default.
- W2762156722 date "2017-10-07" @default.
- W2762156722 modified "2023-09-27" @default.
- W2762156722 title "On the interplay between hypergeometric functions, complete elliptic integrals and Fourier-Legendre series expansions" @default.
- W2762156722 cites W1977875502 @default.
- W2762156722 cites W1991692696 @default.
- W2762156722 cites W2009085226 @default.
- W2762156722 cites W2020405648 @default.
- W2762156722 cites W2030433895 @default.
- W2762156722 cites W2043220612 @default.
- W2762156722 cites W2085489764 @default.
- W2762156722 cites W2100277009 @default.
- W2762156722 cites W2160956159 @default.
- W2762156722 cites W2609082739 @default.
- W2762156722 cites W2963491596 @default.
- W2762156722 cites W2964021239 @default.
- W2762156722 cites W635067416 @default.
- W2762156722 hasPublicationYear "2017" @default.
- W2762156722 type Work @default.
- W2762156722 sameAs 2762156722 @default.
- W2762156722 citedByCount "2" @default.
- W2762156722 countsByYear W27621567222018 @default.
- W2762156722 countsByYear W27621567222023 @default.
- W2762156722 crossrefType "posted-content" @default.
- W2762156722 hasAuthorship W2762156722A5000663767 @default.
- W2762156722 hasAuthorship W2762156722A5066938892 @default.
- W2762156722 hasAuthorship W2762156722A5078146626 @default.
- W2762156722 hasConcept C111458787 @default.
- W2762156722 hasConcept C114614502 @default.
- W2762156722 hasConcept C134306372 @default.
- W2762156722 hasConcept C143724316 @default.
- W2762156722 hasConcept C151730666 @default.
- W2762156722 hasConcept C153262748 @default.
- W2762156722 hasConcept C176671685 @default.
- W2762156722 hasConcept C197320386 @default.
- W2762156722 hasConcept C202444582 @default.
- W2762156722 hasConcept C207864730 @default.
- W2762156722 hasConcept C33923547 @default.
- W2762156722 hasConcept C52704855 @default.
- W2762156722 hasConcept C73749972 @default.
- W2762156722 hasConcept C86803240 @default.
- W2762156722 hasConceptScore W2762156722C111458787 @default.
- W2762156722 hasConceptScore W2762156722C114614502 @default.
- W2762156722 hasConceptScore W2762156722C134306372 @default.
- W2762156722 hasConceptScore W2762156722C143724316 @default.
- W2762156722 hasConceptScore W2762156722C151730666 @default.
- W2762156722 hasConceptScore W2762156722C153262748 @default.
- W2762156722 hasConceptScore W2762156722C176671685 @default.
- W2762156722 hasConceptScore W2762156722C197320386 @default.
- W2762156722 hasConceptScore W2762156722C202444582 @default.
- W2762156722 hasConceptScore W2762156722C207864730 @default.
- W2762156722 hasConceptScore W2762156722C33923547 @default.
- W2762156722 hasConceptScore W2762156722C52704855 @default.
- W2762156722 hasConceptScore W2762156722C73749972 @default.
- W2762156722 hasConceptScore W2762156722C86803240 @default.
- W2762156722 hasLocation W27621567221 @default.
- W2762156722 hasOpenAccess W2762156722 @default.
- W2762156722 hasPrimaryLocation W27621567221 @default.
- W2762156722 hasRelatedWork W1587523919 @default.
- W2762156722 hasRelatedWork W1972013449 @default.
- W2762156722 hasRelatedWork W1979606325 @default.
- W2762156722 hasRelatedWork W1989967254 @default.
- W2762156722 hasRelatedWork W2008090238 @default.
- W2762156722 hasRelatedWork W2008338281 @default.
- W2762156722 hasRelatedWork W2030387385 @default.
- W2762156722 hasRelatedWork W2050732124 @default.
- W2762156722 hasRelatedWork W2093899607 @default.
- W2762156722 hasRelatedWork W2172168998 @default.
- W2762156722 hasRelatedWork W2491953641 @default.
- W2762156722 hasRelatedWork W2738986664 @default.
- W2762156722 hasRelatedWork W2950705685 @default.
- W2762156722 hasRelatedWork W2951567186 @default.
- W2762156722 hasRelatedWork W2963767955 @default.
- W2762156722 hasRelatedWork W2995613335 @default.
- W2762156722 hasRelatedWork W3012102663 @default.
- W2762156722 hasRelatedWork W3129293026 @default.
- W2762156722 hasRelatedWork W3214207438 @default.
- W2762156722 hasRelatedWork W3214308132 @default.
- W2762156722 isParatext "false" @default.
- W2762156722 isRetracted "false" @default.
- W2762156722 magId "2762156722" @default.
- W2762156722 workType "article" @default.