scipy.special.elliprd#
- scipy.special.elliprd(x, y, z) = <ufunc 'elliprd'>#
Symmetric elliptic integral of the second kind.
The function RD is defined as [1]
\[R_{\mathrm{D}}(x, y, z) = \frac{3}{2} \int_0^{+\infty} [(t + x) (t + y)]^{-1/2} (t + z)^{-3/2} dt\]- Parameters
- x, y, zarray_like
Real or complex input parameters. x or y can be any number in the complex plane cut along the negative real axis, but at most one of them can be zero, while z must be non-zero.
- Returns
- Rndarray
Value of the integral. If all of x, y, and z are real, the return value is real. Otherwise, the return value is complex.
See also
Notes
RD is a degenerate case of the elliptic integral RJ:
elliprd(x, y, z) == elliprj(x, y, z, z).The code implements Carlson’s algorithm based on the duplication theorems and series expansion up to the 7th order. [2]
New in version 1.8.0.
References
- 1
B. C. Carlson, ed., Chapter 19 in “Digital Library of Mathematical Functions,” NIST, US Dept. of Commerce. https://dlmf.nist.gov/19.16.E5
- 2
B. C. Carlson, “Numerical computation of real or complex elliptic integrals,” Numer. Algorithm, vol. 10, no. 1, pp. 13-26, 1995. https://arxiv.org/abs/math/9409227 https://doi.org/10.1007/BF02198293