|
In mathematics, a Barnes integral or Mellin–Barnes integral is a contour integral involving a product of gamma functions. They were introduced by . 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''). ==Hypergeometric series== The hypergeometric function is given as a Barnes integral by : This equality can be obtained by moving the contour to the right while picking up the residues at ''s'' = 0, 1, 2, ... . Given proper convergence conditions, one can relate more general Barnes' integrals and generalized hypergeometric functions ''p''''F''''q'' in a similar way. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Barnes integral」の詳細全文を読む スポンサード リンク
|