Arithmatical consequences of two identities of B. Gordon
From two partition identities of Basil Gordon the author derives two recursive formulas for the sum-of-divisors function. A third application yields an alternate proof of Rmanujan's theorem on the divisibility of certain values of the partition function by the modulus 5.
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1979-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171279000508 |
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Article |
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doaj-9e27ae2e32d642549b58735ed9e4822e2020-11-24T22:52:43ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251979-01-012467768410.1155/S0161171279000508Arithmatical consequences of two identities of B. GordonJohn A. Ewell0Department of Mathematical Sciences, Northern Illinois University, Dekalb 60115, Illinois, USAFrom two partition identities of Basil Gordon the author derives two recursive formulas for the sum-of-divisors function. A third application yields an alternate proof of Rmanujan's theorem on the divisibility of certain values of the partition function by the modulus 5.http://dx.doi.org/10.1155/S0161171279000508partition identitiessum-of-divisors functionpartition functionrecurrences. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
John A. Ewell |
| spellingShingle |
John A. Ewell Arithmatical consequences of two identities of B. Gordon International Journal of Mathematics and Mathematical Sciences partition identities sum-of-divisors function partition function recurrences. |
| author_facet |
John A. Ewell |
| author_sort |
John A. Ewell |
| title |
Arithmatical consequences of two identities of B. Gordon |
| title_short |
Arithmatical consequences of two identities of B. Gordon |
| title_full |
Arithmatical consequences of two identities of B. Gordon |
| title_fullStr |
Arithmatical consequences of two identities of B. Gordon |
| title_full_unstemmed |
Arithmatical consequences of two identities of B. Gordon |
| title_sort |
arithmatical consequences of two identities of b. gordon |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1979-01-01 |
| description |
From two partition identities of Basil Gordon the author derives two recursive formulas for the sum-of-divisors function. A third application yields an alternate proof of Rmanujan's theorem on the divisibility of certain values of the partition function by the modulus 5. |
| topic |
partition identities sum-of-divisors function partition function recurrences. |
| url |
http://dx.doi.org/10.1155/S0161171279000508 |
| work_keys_str_mv |
AT johnaewell arithmaticalconsequencesoftwoidentitiesofbgordon |
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1725664796223733760 |