Some theorems on the explicit evaluation of Ramanujan's theta-functions
Bruce C. Berndt et al. and Soon-Yi Kang have proved many of Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions in terms of Weber-Ramanujan class invariants. In this note, we give alternative proofs of some of these identities of theta...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204111058 |
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| author | Nayandeep Deka Baruah P. Bhattacharyya |
| author_facet | Nayandeep Deka Baruah P. Bhattacharyya |
| author_sort | Nayandeep Deka Baruah |
| collection | DOAJ |
| description | Bruce C. Berndt et al. and Soon-Yi Kang have proved many of Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions in terms of Weber-Ramanujan class invariants. In this note, we give alternative proofs of some of these identities of theta-functions recorded by Ramanujan in his notebooks and deduce some formulas for the explicit evaluation of his theta-functions in terms of Weber-Ramanujan class invariants. |
| format | Article |
| id | doaj-art-1a13dd1e247241cdab93f43e6150dd4b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-1a13dd1e247241cdab93f43e6150dd4b2025-02-03T01:03:20ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004402149215910.1155/S0161171204111058Some theorems on the explicit evaluation of Ramanujan's theta-functionsNayandeep Deka Baruah0P. Bhattacharyya1Department of Mathematical Sciences, Tezpur University, Napaam 784 028, Sonitpur, Assam, IndiaDepartment of Mathematical Sciences, Tezpur University, Napaam 784 028, Sonitpur, Assam, IndiaBruce C. Berndt et al. and Soon-Yi Kang have proved many of Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions in terms of Weber-Ramanujan class invariants. In this note, we give alternative proofs of some of these identities of theta-functions recorded by Ramanujan in his notebooks and deduce some formulas for the explicit evaluation of his theta-functions in terms of Weber-Ramanujan class invariants.http://dx.doi.org/10.1155/S0161171204111058 |
| spellingShingle | Nayandeep Deka Baruah P. Bhattacharyya Some theorems on the explicit evaluation of Ramanujan's theta-functions International Journal of Mathematics and Mathematical Sciences |
| title | Some theorems on the explicit evaluation of Ramanujan's theta-functions |
| title_full | Some theorems on the explicit evaluation of Ramanujan's theta-functions |
| title_fullStr | Some theorems on the explicit evaluation of Ramanujan's theta-functions |
| title_full_unstemmed | Some theorems on the explicit evaluation of Ramanujan's theta-functions |
| title_short | Some theorems on the explicit evaluation of Ramanujan's theta-functions |
| title_sort | some theorems on the explicit evaluation of ramanujan s theta functions |
| url | http://dx.doi.org/10.1155/S0161171204111058 |
| work_keys_str_mv | AT nayandeepdekabaruah sometheoremsontheexplicitevaluationoframanujansthetafunctions AT pbhattacharyya sometheoremsontheexplicitevaluationoframanujansthetafunctions |