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Multiple gamma and related functions. (English) Zbl 1026.33003

The multiple Barnes function \(G_n(z)\) obeys the functional equation \[ G_{n+1}(z+1)=G_n(z)G_{n+1}(z), \] with initial conditions \(G_1(z)=\Gamma(z)\), \(G_n(1)=1.\) In this interesting article, a large number of properties of \(G_2(z)\), \(G_3(z)\) and some related functions are surveyed, and some new formulas are given.

MSC:

33B15 Gamma, beta and polygamma functions
33C99 Hypergeometric functions
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