mars.tensor.special.kv#

mars.tensor.special.kv(v, z, **kwargs)[source]#

Modified Bessel function of the second kind of real order v

Returns the modified Bessel function of the second kind for real order v at complex z.

These are also sometimes called functions of the third kind, Basset functions, or Macdonald functions. They are defined as those solutions of the modified Bessel equation for which,

\[K_v(x) \sim \sqrt{\pi/(2x)} \exp(-x)\]

as \(x \to \infty\) 3.

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 – The results. Note that input must be of complex type to get complex output, e.g. kv(3, -2+0j) instead of kv(3, -2).

Return type

ndarray

Notes

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

See also

kve

This function with leading exponential behavior stripped off.

kvp

Derivative of this function

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

3

NIST Digital Library of Mathematical Functions, Eq. 10.25.E3. https://dlmf.nist.gov/10.25.E3