A variation of multiple $L$-values arising from the spectral zeta function of the non-commutative harmonic oscillator

Kazufumi Kimoto, Yoshinori Yamasaki

Published 2007-12-12, updated 2008-05-08Version 2

A variation of multiple $L$-values, which arises from the description of the special values of the spectral zeta function of the non-commutative harmonic oscillator, is introduced. In some special cases, we show that its generating function can be written in terms of the gamma functions. This result enables us to obtain explicit evaluations of them.