Number theory | Special functions
Barnes G-function
In mathematics, the Barnes G-function G(z) is a function that is an extension of superfactorials to the complex numbers. It is related to the gamma function, the K-function and the Glaisher–Kinkelin constant, and was named after mathematician Ernest William Barnes. It can be written in terms of the double gamma function. Formally, the Barnes G-function is defined in the following Weierstrass product form: where is the Euler–Mascheroni constant, exp(x) = ex is the exponential function, and Π denotes multiplication (capital pi notation). As an entire function, G is of order two, and of infinite type. This can be deduced from the asymptotic expansion given below. (Wikipedia).
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