maxframe.tensor.special.elliprc#

maxframe.tensor.special.elliprc(x, y, **kwargs)[source]#

Degenerate symmetric elliptic integral.

The function RC is defined as [1]

\[R_{\mathrm{C}}(x, y) = \frac{1}{2} \int_0^{+\infty} (t + x)^{-1/2} (t + y)^{-1} dt = R_{\mathrm{F}}(x, y, y)\]
Parameters:

  • x (array_like) – Real or complex input parameters. x can be any number in the complex plane cut along the negative real axis. y must be non-zero.

  • y (array_like) – Real or complex input parameters. x can be any number in the complex plane cut along the negative real axis. y must be non-zero.

  • out (ndarray, optional) – Optional output array for the function values

Returns:

R – Value of the integral. If y is real and negative, the Cauchy principal value is returned. If both of x and y are real, the return value is real. Otherwise, the return value is complex.

Return type:

scalar or ndarray

See also

elliprf

Completely-symmetric elliptic integral of the first kind.

elliprd

Symmetric elliptic integral of the second kind.

elliprg

Completely-symmetric elliptic integral of the second kind.

elliprj

Symmetric elliptic integral of the third kind.

Notes

RC is a degenerate case of the symmetric integral RF: elliprc(x, y) == elliprf(x, y, y). It is an elementary function rather than an elliptic integral.

The code implements Carlson’s algorithm based on the duplication theorems and series expansion up to the 7th order. [2]

References