New identities for ratios of Ramanujan’s theta function
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Ramanujan in his notebooks, has established several new modular equation which he denoted as P and Q. In this paper, we establish several new identities for ratios of Ramanujan’s theta function involving φ(q). We establish some new explicit evaluations for the ratios of Ramanujan’s theta function. We also establish some new modular relations for a continued fraction of order twelve H(q) with H(qn) for n =2, 4, 6, 8, 10, 12, 14 and 16.
Abstract
Ramanujan in his notebooks, has established several new modular equation which he denoted as P and Q. In this paper, we establish several new identities for ratios of Ramanujan’s theta function involving φ(q). We establish some new explicit evaluations for the ratios of Ramanujan’s theta function. We also establish some new modular relations for a continued fraction of order twelve H(q) with H(qn) for n =2, 4, 6, 8, 10, 12, 14 and 16.
참고문헌 (12)
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