scipy.special.kve

scipy.special.kve(v, z, out=None) = <ufunc 'kve'>

Exponentially scaled modified Bessel function of the second kind.

Returns the exponentially scaled, modified Bessel function of the second kind (sometimes called the third kind) for real order v at complex z:

kve(v, z) = kv(v, z) * exp(z)

Parameters

varray_like of float

Order of Bessel functions

zarray_like of complex

Argument at which to evaluate the Bessel functions

outndarray, optional

Optional output array for the function results

Returns

scalar or ndarray

The exponentially scaled modified Bessel function of the second kind.

Notes

Wrapper for AMOS [1] routine zbesk. For a discussion of the algorithm used, see [2] and the references therein.

References

1

Donald E. Amos, “AMOS, A Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order”, http://netlib.org/amos/

2

Donald E. Amos, “Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order”, ACM TOMS Vol. 12 Issue 3, Sept. 1986, p. 265