Transformation formulae for multiple series
R. Sitaramachandra Rao, M. V. Subba Rao · Pacific Journal of Mathematics · 1984
In this paper we prove a general transformation formula for a triple series of complex terms.We deduce a transformation formula for double series and discuss some applications.Furthermore, some reciprocity relations of the following type are obtained: Let a, b y c be reals greater than 1 and P(a,b,c) = 2 r~a 2 k ~b Σ ι ~c-r=\ k=\ l=\ Then P(a, b, c) + P(a, c, b) + P(b, c, a) + P(b, a, c) + ζ(b)ζ(c + a) + ζ(c)S(a + b) + 2{(β + * + c), where f denotes the Riemann zeta function.In particular, P(2,2,2) = 31ττ 6 /15,12O.