mars.tensor.special.kv#
- mars.tensor.special.kv(v, z, **kwargs)[源代码]#
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.
- 参数
- 返回
out – The results. Note that input must be of complex type to get complex output, e.g.
kv(3, -2+0j)
instead ofkv(3, -2)
.- 返回类型
ndarray
备注
Wrapper for AMOS 1 routine zbesk. For a discussion of the algorithm used, see 2 and the references therein.
参见
kve
This function with leading exponential behavior stripped off.
kvp
Derivative of this function
引用
- 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