Matches in SemOpenAlex for { <https://semopenalex.org/work/W4241295865> ?p ?o ?g. }
Showing items 1 to 47 of
47
with 100 items per page.
- W4241295865 endingPage "993" @default.
- W4241295865 startingPage "993" @default.
- W4241295865 abstract "The aim of this paper is to show that the Minakshisundaram-Pleijel zeta function ${Z_k}(s)$ of k-dimensional sphere ${mathbb {S}^k},k geq 2$ (defined in $Re e(s) > frac {k}{2}$ by [ {Z_k}(s) = sum limits _{n = 1}^infty {frac {{{P_k}(n)}}{{{{[n(n + k - 1)]}^s}}}} ] with $(k - 1)!{P_k}(n) = mathcal {R}(n + 1,k - 2)(2n + k - 1)$ where the rising factorial $mathcal {R}(x,n) = x(x + 1) cdots (x + n - 1)$ is defined for real number x and n nonnegative integer) can be put in the form [ (k - 1)!{Z_k}(s) = {sum limits _{l = 0}^infty {{{( - 1)}^l}left ( {frac {{k - 1}}{2}} right )} ^{2l}}left ( {begin {array}{*{20}{c}} { - s} l end {array} } right )sum limits _{j = 0}^{k - 1} {{B_{k,}}_jzeta (2s + 2l - j,frac {{k + 1}}{2})} ] where ${B_{k,j}}$ are explicitly computed. The above formula allows us to find explicitly the residue of ${Z_k}(s)$ at the pole $s = frac {k}{2} - n,n in mathbb {N}$, [ frac {1}{{(k - 1)!}}sum limits _{h = 0}^{frac {k}{2} - 1} {{{sum limits _{begin {array}{*{20}{c}} {l + h = n} {l geq 0} end {array} } {{{( - 1)}^l}left ( {frac {{k - 1}}{2}} right )} }^{2l}}left ( {begin {array}{*{20}{c}} {n - frac {k}{2}} l end {array} } right )} {B_{k,k - 2h - 1}}.] In passing, we also obtain apparently new relations among the Stirling numbers." @default.
- W4241295865 created "2022-05-12" @default.
- W4241295865 creator A5037209290 @default.
- W4241295865 creator A5083825434 @default.
- W4241295865 date "1994-12-01" @default.
- W4241295865 modified "2023-09-27" @default.
- W4241295865 title "On Minakshisundaram-Pleijel Zeta Functions of Spheres" @default.
- W4241295865 doi "https://doi.org/10.2307/2161165" @default.
- W4241295865 hasPublicationYear "1994" @default.
- W4241295865 type Work @default.
- W4241295865 citedByCount "1" @default.
- W4241295865 crossrefType "journal-article" @default.
- W4241295865 hasAuthorship W4241295865A5037209290 @default.
- W4241295865 hasAuthorship W4241295865A5083825434 @default.
- W4241295865 hasBestOaLocation W42412958651 @default.
- W4241295865 hasConcept C114614502 @default.
- W4241295865 hasConcept C121332964 @default.
- W4241295865 hasConcept C199360897 @default.
- W4241295865 hasConcept C33923547 @default.
- W4241295865 hasConcept C41008148 @default.
- W4241295865 hasConcept C97137487 @default.
- W4241295865 hasConceptScore W4241295865C114614502 @default.
- W4241295865 hasConceptScore W4241295865C121332964 @default.
- W4241295865 hasConceptScore W4241295865C199360897 @default.
- W4241295865 hasConceptScore W4241295865C33923547 @default.
- W4241295865 hasConceptScore W4241295865C41008148 @default.
- W4241295865 hasConceptScore W4241295865C97137487 @default.
- W4241295865 hasIssue "4" @default.
- W4241295865 hasLocation W42412958651 @default.
- W4241295865 hasOpenAccess W4241295865 @default.
- W4241295865 hasPrimaryLocation W42412958651 @default.
- W4241295865 hasRelatedWork W1967784590 @default.
- W4241295865 hasRelatedWork W1978042415 @default.
- W4241295865 hasRelatedWork W2017331178 @default.
- W4241295865 hasRelatedWork W2044215988 @default.
- W4241295865 hasRelatedWork W2123715679 @default.
- W4241295865 hasRelatedWork W2320229756 @default.
- W4241295865 hasRelatedWork W2327497304 @default.
- W4241295865 hasRelatedWork W2329128713 @default.
- W4241295865 hasRelatedWork W2976797620 @default.
- W4241295865 hasRelatedWork W3086542228 @default.
- W4241295865 hasVolume "122" @default.
- W4241295865 isParatext "false" @default.
- W4241295865 isRetracted "false" @default.
- W4241295865 workType "article" @default.