The IMSL_ELRJ function evaluates Carlson’s elliptic integral of the third kind RJ (x, y, z, ρ).
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Carlson’s elliptic integral of the third kind is defined to be:
The arguments must be nonnegative. In addition, x + y, x + z, y + z and ρ must be greater than or equal to (5s)1/3 and less than or equal to 0.3(b/5)1/3, where s is the smallest representable floating-point number. Should any of these conditions fail IMSL_ELRJ is set to b, the largest floating-point number.
The IMSL_ELRJ function is based on the code by Carlson and Notis (1981) and the work of Carlson (1979).
Example
The integral RJ (2, 3, 4, 5) is computed.
PRINT, IMSL_ELRJ(2.0, 3.0, 4.0, 5.0)
0.142976
Syntax
Result = IMSL_ELRJ(X, Y, Z, Rho [, /DOUBLE]
Return Value
The complete elliptic integral RJ (x, y, z, ρ).
Arguments
Rho
Fourth argument for which the function value is desired. It must be positive.
X
First argument for which the function value is desired. It must be nonnegative.
Y
Second argument for which the function value is desired. It must be nonnegative.
Z
Third argument for which the function value is desired. It must be positive.
Keywords
DOUBLE (optional)
If present and nonzero, double precision is used.
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