Shintani – Barnes zeta and gamma functions

@inproceedings{Friedman2004ShintaniB,
  title={Shintani – Barnes zeta and gamma functions},
  author={Eduardo Friedman and Simon M. Ruijsenaars and Takahiro Kawai},
  year={2004}
}
We show that Shintani’s work on multiple zeta and gamma functions can be simplified and extended by exploiting difference equations. We re-prove many of Shintani’s formulas and prove several new ones. Among the latter is a generalization to the Shintani–Barnes gamma functions of Raabe’s 1843 formula R 1 0 log GðxÞ dx 1⁄4 log ffiffiffiffiffi 2p p ; and a further generalization to the Shintani zeta functions. These explicit formulas can be interpreted as ‘‘vanishing period integral’’ side… CONTINUE READING

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