ellint_rj

kyosu::ellint_rj = eve::functor<ellint_rj_t>

inlineconstexpr

Computes the Carlson's elliptic integral \( \mathbf{R}_\mathbf{J}(x, y) = \frac32 \int_{0}^{\infty} \scriptstyle(t+p)^{-1}[(t+x)(t+y)(t+z)]^{-1/2}\scriptstyle\;\mathrm{d}t\).

Header file

#include <eve/module/elliptic.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto ellint_rj(auto x, auto y, auto z, auto p)                          noexcept; // 1
 
   // semantic modifier
   constexpr auto ellint_rj[threshold = tol](auto x, auto y, auto z, auto p)         noexcept; // 1
 
   // Lanes masking
   constexpr auto ellint_rj[conditional_expr auto c](auto x, auto y, auto z, auto p) noexcept; // 2
   constexpr auto ellint_rj[logical_value auto m](auto x, auto y, auto z, auto p)    noexcept; // 2
}

Parameters

• x, y, z: floating real arguments.
• p: floating real arguments.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

1. the value of the \(\mathbf{R}_\mathbf{J}\) Carlson elliptic integral: \( \frac32 \int_{0}^{\infty} \scriptstyle(t+p)^{-1}[(t+x)(t+y)(t+z)]^{-1/2}\;\mathrm{d}t\) is returned with relative error less in magnitude than tol (default to eps), The integral is well defined if x, y, z lie in the complex plane cut along the nonpositive real axis, with the exception that at at most one of x, y, z can be 0.
2. The operation is performed conditionnaly

External references

• DLMF: Elliptic Integrals
• Wolfram MathWorld: Elliptic Integral

Example