ellipticIntegralRC¶
Evaluates an elementary integral from which inverse circular functions, logarithms and inverse hyperbolic functions can be computed.
Synopsis¶
ellipticIntegralRC (x, y)
Required Arguments¶
- float
x
(Input) - First variable of the incomplete elliptic integral. It must be nonnegative and must satisfy the conditions given below.
- float
y
(Input) - Second variable of the incomplete elliptic integral. It must be positive and must satisfy the conditions given below.
Return Value¶
The elliptic integral \(R_C(x,y)\).
Description¶
Carlson’s elliptic integral of the third kind is defined to be
\[R_C(x,y) = \tfrac{1}{2} \int_0^{\infty}
\frac{dt}{\left[(t+x)(t+y)^2\right]^{1/2}}\]
The argument x must be nonnegative, y must be positive, and x +y
must be less than or equal to b/5 and greater than or equal to 5s.
If any of these conditions are false, the ellipticIntegralRC
is set to
b. Here, b = machine(2)
is the largest and s = machine(1)
is
the smallest representable floating-point number. For more information, see
the description for machine.
The function ellipticIntegralRC
is based on the code by Carlson and
Notis (1981) and the work of Carlson (1979).