## S Kanemitsu ; Y Tanigawa ; H Tsukada - On Kronecker's limit formula and the hypergeometric function.

hrj:163 - Hardy-Ramanujan Journal, January 1, 2008, Volume 31 - 2008 - https://doi.org/10.46298/hrj.2008.163
On Kronecker's limit formula and the hypergeometric function.

Authors: S Kanemitsu ; Y Tanigawa ; H Tsukada

The Kronecker limit formula for a positive definite binary quadratic form or the Dedekind zeta-function of an imaginary quadratic field is quite well-known and there exists an enormous amount of literature pertaining to its proof and applications. Here we give a different kind of proof depending on the hypergeometric transform. The idea goes back to Koshilyakov and we adopted it in this note to give a new derivation of the formula. Here the connection formula for the hypergeometric function plays an essential role.

Volume: Volume 31 - 2008
Published on: January 1, 2008
Imported on: March 3, 2015
Keywords: connection formula, hypergeometric function, hypergeometric transform, Dedekind zeta-function,Kronecker limit formula, positive definite binary quadratic form,[MATH] Mathematics [math]