Analogues of a Transformation Formula of Ramanujan
نویسنده
چکیده
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 formula, we derive the transformation formula of Ramanujan.
منابع مشابه
Character Analogues of Theorems of Ramanujan, Koshliakov and Guinand
We derive analogues of theorems of Ramanujan, Koshliakov and Guinand for primitive characters. As particular examples, transformation formulas involving the Legendre symbol and sums-of-divisors functions are established.
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