International Journal of Number Theory · 2011 · 19 citations · 2 references
Natural SciencesMathematicsAlgebraCombinatoricsNumber TheoryGenerating FunctionsModular ArithmeticModular FormsExplicit FormulaeGamma FunctionRiemann Zeta Function
We derive two new analogues of a transformation formula of Ramanujan involving the Gamma function and Riemann zeta function present in his Lost Notebook. Both involve infinite series consisting of Hurwitz zeta functions and yield modular-type 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.
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