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

Shintani–Barnes zeta and gamma functions - ResearchGate. Available from: http://www.researchgate.net/publication/222699495_ShintaniBarnes_zeta_and_gamma_functions [accessed Oct 3, 2015].