10.46298/hrj.2008.163
https://hrj.episciences.org/163
Kanemitsu, S
S
Kanemitsu
Tanigawa, Y
Y
Tanigawa
Tsukada, H
H
Tsukada
On Kronecker's limit formula and the hypergeometric function.
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.
episciences.org
connection formula
hypergeometric function
hypergeometric transform
Dedekind zeta-function
Kronecker limit formula
positive definite binary quadratic form
[MATH] Mathematics [math]
2015-06-12
2008-01-01
2008-01-01
en
journal article
https://hal.archives-ouvertes.fr/hal-01112329v1
2804-7370
https://hrj.episciences.org/163/pdf
VoR
application/pdf
Hardy-Ramanujan Journal
Volume 31 - 2008
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