Matches in SemOpenAlex for { <https://semopenalex.org/work/W2953644865> ?p ?o ?g. }
Showing items 1 to 78 of
78
with 100 items per page.
- W2953644865 abstract "Andrews and Bressoud, Alladi and Gordon, and others, have proven, in a number of papers, that the coefficients in various arithmetic progressions in the series expansions of certain infinite $q$-products vanish. In the present paper it is shown that these results follow automatically (simply by specializing parameters) in an identity derived from a special case of Ramanujan's $_1psi_1$ identity. Likewise, a number of authors have proven results about the $m$-dissections of certain infinite $q$-products using various methods. It is shown that many of these $m$-dissections also follow automatically (again simply by specializing parameters) from this same identity alluded to above. Two identities that mat be considered as extensions of two Identities of Ramanujan are also derived. It is also shown how applying similar ideas to certain other Lambert series gives rise to some rather curious $q$-series identities, such as, for any positive integer $m$, begin{multline*} {displaystyle frac{left(q,q,a,frac{q}{a},frac{b q}{d}, frac{dq}{b}, frac{aq}{b d}, frac{b d q}{a};qright)_{infty }} {left(b,frac{q}{b},d,frac{q}{d},frac{a}{b},frac{bq}{a},frac{a}{d},frac{dq}{a};qright)_{infty }}} = sum _{r=0}^{m-1} q^r frac{ left(q^m,q^m,a q^{2 r},frac{q^{m-2 r}}{a},frac{b q^m}{d},frac{d q^m}{b}, frac{a q^m}{b d},frac{b dq^m}{a};q^mright){}_{infty }} {left(b q^r,frac{q^{m-r}}{b},d q^r,frac{q^{m-r}}{d},frac{a q^r}{b},frac{b q^{m-r}}{a},frac{a q^r}{d}, frac{dq^{m-r}}{a};q^mright){}_{infty }} end{multline*} and begin{equation*} (aq;q)_{infty}sum_{n=1}^{infty} frac{n a^n q^{n}}{(q;q)_n} = sum_{r=1}^{m}(aq^{r};q^m)_{infty}sum_{n=1}^{infty} frac{na^n q^{n r}}{(q^m;q^m)_n}. end{equation*} Applications to the Fine function $F(a,b;t)$ are also considered." @default.
- W2953644865 created "2019-07-12" @default.
- W2953644865 creator A5059271041 @default.
- W2953644865 date "2019-06-27" @default.
- W2953644865 modified "2023-09-27" @default.
- W2953644865 title "Some Observations on Lambert series, vanishing coefficients and dissections of infinite products and series" @default.
- W2953644865 cites W122926215 @default.
- W2953644865 cites W1970169851 @default.
- W2953644865 cites W1999803716 @default.
- W2953644865 cites W2051360792 @default.
- W2953644865 cites W2059140607 @default.
- W2953644865 cites W2085219949 @default.
- W2953644865 cites W2101544726 @default.
- W2953644865 cites W2118983419 @default.
- W2953644865 cites W2135643877 @default.
- W2953644865 cites W2142116576 @default.
- W2953644865 cites W2155804742 @default.
- W2953644865 cites W2185334019 @default.
- W2953644865 cites W2587442072 @default.
- W2953644865 cites W2791465356 @default.
- W2953644865 hasPublicationYear "2019" @default.
- W2953644865 type Work @default.
- W2953644865 sameAs 2953644865 @default.
- W2953644865 citedByCount "1" @default.
- W2953644865 countsByYear W29536448652020 @default.
- W2953644865 crossrefType "posted-content" @default.
- W2953644865 hasAuthorship W2953644865A5059271041 @default.
- W2953644865 hasConcept C114614502 @default.
- W2953644865 hasConcept C121332964 @default.
- W2953644865 hasConcept C131220774 @default.
- W2953644865 hasConcept C143724316 @default.
- W2953644865 hasConcept C151730666 @default.
- W2953644865 hasConcept C199360897 @default.
- W2953644865 hasConcept C24890656 @default.
- W2953644865 hasConcept C2778355321 @default.
- W2953644865 hasConcept C33923547 @default.
- W2953644865 hasConcept C41008148 @default.
- W2953644865 hasConcept C86803240 @default.
- W2953644865 hasConcept C97137487 @default.
- W2953644865 hasConceptScore W2953644865C114614502 @default.
- W2953644865 hasConceptScore W2953644865C121332964 @default.
- W2953644865 hasConceptScore W2953644865C131220774 @default.
- W2953644865 hasConceptScore W2953644865C143724316 @default.
- W2953644865 hasConceptScore W2953644865C151730666 @default.
- W2953644865 hasConceptScore W2953644865C199360897 @default.
- W2953644865 hasConceptScore W2953644865C24890656 @default.
- W2953644865 hasConceptScore W2953644865C2778355321 @default.
- W2953644865 hasConceptScore W2953644865C33923547 @default.
- W2953644865 hasConceptScore W2953644865C41008148 @default.
- W2953644865 hasConceptScore W2953644865C86803240 @default.
- W2953644865 hasConceptScore W2953644865C97137487 @default.
- W2953644865 hasLocation W29536448651 @default.
- W2953644865 hasOpenAccess W2953644865 @default.
- W2953644865 hasPrimaryLocation W29536448651 @default.
- W2953644865 hasRelatedWork W1979567118 @default.
- W2953644865 hasRelatedWork W1983146314 @default.
- W2953644865 hasRelatedWork W2059412210 @default.
- W2953644865 hasRelatedWork W2061000403 @default.
- W2953644865 hasRelatedWork W2187311322 @default.
- W2953644865 hasRelatedWork W2508978482 @default.
- W2953644865 hasRelatedWork W2626211028 @default.
- W2953644865 hasRelatedWork W2786812595 @default.
- W2953644865 hasRelatedWork W2913185030 @default.
- W2953644865 hasRelatedWork W2963807416 @default.
- W2953644865 hasRelatedWork W2999388462 @default.
- W2953644865 hasRelatedWork W3013186486 @default.
- W2953644865 hasRelatedWork W3044524978 @default.
- W2953644865 hasRelatedWork W3092146183 @default.
- W2953644865 hasRelatedWork W3099001047 @default.
- W2953644865 hasRelatedWork W3101100069 @default.
- W2953644865 hasRelatedWork W3134385715 @default.
- W2953644865 hasRelatedWork W3190940978 @default.
- W2953644865 hasRelatedWork W3203284814 @default.
- W2953644865 hasRelatedWork W832554380 @default.
- W2953644865 isParatext "false" @default.
- W2953644865 isRetracted "false" @default.
- W2953644865 magId "2953644865" @default.
- W2953644865 workType "article" @default.