ellint_rf

kyosu::ellint_rf = eve::functor<ellint_rf_t>

inlineconstexpr

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

Header file

#include <eve/module/elliptic.hpp>

Callable Signatures

namespace eve
{
   // Regular overload
   constexpr auto ellint_rf(auto x, auto y, auto z)                           noexcept; // 1
 
   // Lanes masking
   constexpr auto ellint_rf[conditional_expr auto c](auto x, auto y, auto z) noexcept; // 2
   constexpr auto ellint_rf[logical_value auto m](auto x, auto y, auto z)    noexcept; // 2
}

Parameters

• x, y, z: Can be a mix of complex and real floating values.
• c: Conditional expression masking the operation.
• m: Logical value masking the operation.

Return value

1. the value of the \(\mathbf{R}_\mathbf{F}\) Carlson elliptic integral: \( \frac32 \int_{0}^{\infty} \scriptstyle[(t+x)(t+y)(t+z)]^{-1/2}\scriptstyle\;\mathrm{d}t\). is returned. The integral is well defined if x, y, z lie in the complex plane cut along the nonpositive real axis, with the exception that one of x, y, z must be non 0
2. The operation is performed conditionnaly

External references

• DLMF: Elliptic Integral
• Wolfram MathWorld: Elliptic Integral

Example