In mathematics, a Barnes integral or Mellin–Barnes integral is a contour integral involving a product of gamma functions. They were introduced by Ernest William Barnes (1908, 1910). They are closely related to generalized hypergeometric series.
The integral is usually taken along a contour which is a deformation of the imaginary axis passing to the left of all poles of factors of the form Γ(a + s) and to the right of all poles of factors of the form Γ(a − s).
Read more about Barnes Integral: Hypergeometric Series, Barnes Lemmas, Q-Barnes Integrals
Famous quotes containing the words barnes and/or integral:
“But no. Too soon I voun my charm abroke.
Noo comely soul in white like her
Noo soul a-steppen light like her
An nwone o comely height like her
Went by; but all my grief agean awoke.”
—William Barnes (18011886)
“Painting myself for others, I have painted my inward self with colors clearer than my original ones. I have no more made my book than my book has made mea book consubstantial with its author, concerned with my own self, an integral part of my life; not concerned with some third-hand, extraneous purpose, like all other books.”
—Michel de Montaigne (15331592)