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. Up to elementary factors, it is a special case of the double gamma function.
Formally, the Barnes G-function is defined (in the form of a Weierstrass product) as
where γ is the Euler–Mascheroni constant, exp(x) = ex, and ∏ is capital pi notation.
Read more about Barnes G-function: Difference Equation, Functional Equation and Special Values, Multiplication Formula, Asymptotic Expansion
Famous quotes containing the word barnes:
“We are beginning to wonder whether a servant girl hasn’t the best of it after all. She knows how the salad tastes without the dressing, and she knows how life’s lived before it gets to the parlor door.”
—Djuna Barnes (1892–1982)