The Ramanujan identities under modular substitutions
نویسندگان
چکیده
منابع مشابه
On Plouffe’s Ramanujan Identities
Recently, Simon Plouffe has discovered a number of identities for the Riemann zeta function at odd integer values. These identities are obtained numerically and are inspired by a prototypical series for Apéry’s constant given by Ramanujan: ζ (3) = 7π3 180 −2 ∞ ∑ n=1 1 n3 (e2πn−1) Such sums follow from a general relation given by Ramanujan, which is rediscovered and proved here using complex ana...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1942
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1942-0006204-2