treams.special.intkambe

treams.special.intkambe(n, z, eta) = <ufunc 'intkambe'>

Integral appearing in the accelerated lattice summations

Named here after its appearance (in a slightly different form) in equation (3.16), in Kambe’s paper [1].

This function is defined as

\[I_n(\eta, z) = \int_\eta^\infty t^n \mathrm e^{-\frac{z^2t^2}{2} + \frac{1}{2t^2}} \mathrm d t\]

and is calculated via recursion.

Parameters:
  • n (integer, array_like) – Order

  • z (float or complex, array_like) – Argument

  • eta (float or complex, array_like) – Integral cutoff

Returns:

float or complex

References