10.46298/hrj.2009.166
https://hrj.episciences.org/166
Chakraborty, K
K
Chakraborty
Kanemitsu, S
S
Kanemitsu
Kuzumaki, T
T
Kuzumaki
Finite expressions for higher derivatives of the Dirichlet L-function and the Deninger R-function
We show the equivalence of the finite expression of Deninger's `R-function' at the rational arguments and the Kronecker limit formula on the line of our past study on the Gauss formula for the digamma function and the Dirichlet class number formula. Here the Gauss formula and the class number formula will be replaced by its analogue for the `R-function' and by the Kronecker limit formula or rather a closed form for the derivative of the Dirichlet L-function respectively.
We also make a systematic study of the `$R_k$-function' by appealing to the Lipschitz-Lerch transcendent in which there is the vector space structure built in of these special functions.
episciences.org
Euler digamma function
Generalized Euler constant
Lipschitz-Lerch transcendent
Kronecker limit formula
[MATH] Mathematics [math]
2015-06-12
2009-01-01
2009-01-01
en
journal article
https://hal.archives-ouvertes.fr/hal-01112359v1
2804-7370
https://hrj.episciences.org/166/pdf
VoR
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Hardy-Ramanujan Journal
Volume 32 - 2009
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