A character analogue of Ramanujan’s formula for odd Zeta values

Abstract

Around two decades ago, three Japanese mathematicians Kanemitsu, Tanigawa, and Yoshimoto investigated an infinite series of the following form: X1 m=1 mN where N 2 N and h 2 Z with some restriction on h. Recently, Dixit and Maji pointed out that this series is already present in the lost notebook of Ramanujan with a more general form. Although, Ramanujan did not provide any transforma tion identity for it. Dixit and Maji found an elegant generalization of Ramanu jan’s celebrated identity for ⇣(2m + 1) while extending the results of Kanemitsu et al. Later, Kanemitsu et al. also studied another extended version of the aforementioned series, namely q r=1 X1 n=1 where