{"docId":163,"paperId":163,"url":"https:\/\/hrj.episciences.org\/163","doi":"10.46298\/hrj.2008.163","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":42,"name":"Volume 31 - 2008"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01112329","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01112329v1","dateSubmitted":"2015-03-03 16:14:01","dateAccepted":"2015-06-12 16:05:57","datePublished":"2008-01-01 08:00:00","titles":{"en":"On Kronecker's limit formula and the hypergeometric function."},"authors":["Kanemitsu, S","Tanigawa, Y","Tsukada, H"],"abstracts":{"en":"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."},"keywords":[{"en":" connection formula"},{"en":" hypergeometric function"},{"en":" hypergeometric transform"},{"en":" Dedekind zeta-function"},{"en":"Kronecker limit formula"},{"en":" positive definite binary quadratic form"},"[MATH] Mathematics [math]"]}