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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:
33B15Gamma, beta and polygamma functions
33C99Hypergeometric functions
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References:
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