منابع مشابه
Analogues of a Transformation Formula of Ramanujan
We derive two new analogues of a transformation formula of Ramanujan involving the Gamma and Riemann zeta functions present in the Lost Notebook. Both involve infinite series consisting of Hurwitz zeta functions and yield modular relations. As a special case of the first formula, we obtain an identity involving polygamma functions given by A.P. Guinand and as a limiting case of the second formu...
متن کاملA p-adic analogue of a formula of Ramanujan
During his lifetime, Ramanujan provided many formulae relating binomial sums to special values of the Gamma function. Based on numerical computations, Van Hamme recently conjectured p-adic analogues to such formulae. Using a combination of ordinary and Gaussian hypergeometric series, we prove one of these conjectures. Mathematics Subject Classification (2000). Primary: 33C20; Secondary: 11S80.
متن کاملA Hardy-Ramanujan-Rademacher-type formula for (r, s)-regular partitions
Let pr,s(n) denote the number of partitions of a positive integer n into parts containing no multiples of r or s, where r > 1 and s > 1 are square-free, relatively prime integers. We use classical methods to derive a Hardy-Ramanujan-Rademacher-type infinite series for pr,s(n).
متن کاملCurious Extensions of Ramanujan ’ s
We deduce new q-series identities by applying inverse relations to certain identities for basic hypergeometric series. The identities obtained themselves do not belong to the hierarchy of basic hypergeomet-ric series. We extend two of our identities, by analytic continuation, to bilateral summation formulae which contain Ramanujan's 1 ψ 1 summation and a very-well-poised 4 ψ 6 summation as spec...
متن کاملA Derivation of the Hardy-ramanujan Formula from an Arithmetic Formula
We re-prove the Hardy-Ramanujan asymptotic formula for the partition function without using the circle method. We derive our result from recent work of Bruinier and Ono on harmonic weak Maass forms.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1987
ISSN: 0022-314X
DOI: 10.1016/0022-314x(87)90012-6