SciPy

scipy.special.kve

scipy.special.kve(v, z) = <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:

v : array_like of float

Order of Bessel functions

z : array_like of complex

Argument at which to evaluate the Bessel functions

Returns:

out : ndarray

The exponentially scaled modified Bessel function of the second kind.

Notes

Wrapper for AMOS [R427] routine zbesk. For a discussion of the algorithm used, see [R428] and the references therein.

References

[R427](1, 2) Donald E. Amos, “AMOS, A Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order”, http://netlib.org/amos/
[R428](1, 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

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