![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Plot_of_the_Barnes_G_aka_double_gamma_function_G%2528z%2529_in_the_complex_plane_from_-2-2i_to_2%252B2i_with_colors_created_with_Mathematica_13.1_function_ComplexPlot3D.svg/640px-Plot_of_the_Barnes_G_aka_double_gamma_function_G%2528z%2529_in_the_complex_plane_from_-2-2i_to_2%252B2i_with_colors_created_with_Mathematica_13.1_function_ComplexPlot3D.svg.png&w=640&q=50)
Multiple gamma function
Generalization of the Euler gamma function and the Barnes G-function / From Wikipedia, the free encyclopedia
For derivatives of the log of the gamma function, see polygamma function.
In mathematics, the multiple gamma function is a generalization of the Euler gamma function and the Barnes G-function. The double gamma function was studied by Barnes (1901). At the end of this paper he mentioned the existence of multiple gamma functions generalizing it, and studied these further in Barnes (1904).
![Plot of the Barnes G aka double gamma function G(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D](http://upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Plot_of_the_Barnes_G_aka_double_gamma_function_G%28z%29_in_the_complex_plane_from_-2-2i_to_2%2B2i_with_colors_created_with_Mathematica_13.1_function_ComplexPlot3D.svg/640px-Plot_of_the_Barnes_G_aka_double_gamma_function_G%28z%29_in_the_complex_plane_from_-2-2i_to_2%2B2i_with_colors_created_with_Mathematica_13.1_function_ComplexPlot3D.svg.png)
Double gamma functions are closely related to the q-gamma function, and triple gamma functions
are related to the elliptic gamma function.