A NEW CONVOLUTION IDENTITY DEDUCIBLE FROM THE REMARKABLE FORMULA OF RAMANUJAN

Abstract

In this paper we obtain a convolution identity for the coefficients Bn(α, θ, q) defined by ∞ n=−∞ Bn(α, θ, q)xn = ∞ n=1 (1 + 2xqn cos θ + x2q2n) ∞ n=1 (1 + αqnxeiθ) , using the well-known Ramanujan’s 1ψ1-summation formula. The work presented here complements the works of K.-W. Yang, S. Bhargava, C. Adiga and D. D. Somashekara and of H. M. Srivastava.