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:
“Leaves of the summer, lovely summer’s pride,
Sweet is the shade below your silent tree,”
—William Barnes (1801–1886)
“An island always pleases my imagination, even the smallest, as a small continent and integral portion of the globe. I have a fancy for building my hut on one. Even a bare, grassy isle, which I can see entirely over at a glance, has some undefined and mysterious charm for me.”
—Henry David Thoreau (1817–1862)