CarlsonRG
CarlsonRG[x,y,z]
gives the Carlson's elliptic integral .
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
- For non-negative arguments,
.
- CarlsonRG[x,y,z] has a branch cut discontinuity at
.
- For certain arguments, CarlsonRG automatically evaluates to exact values.
- CarlsonRG can be evaluated to arbitrary precision.
- CarlsonRG automatically threads over lists.
Examples
open allclose allBasic Examples (3)
Plot over a range of arguments:
CarlsonRG is related to Legendre elliptic integral of the second kind for
:
Scope (9)
Numerical Evaluation (5)
Precision of the output tracks the precision of the input:
Evaluate for complex arguments:
Evaluate efficiently at high precision:
CarlsonRG threads elementwise over lists:
Specific Values (2)
Function Representations (1)
TraditionalForm formatting:
Applications (2)
Calculate the surface area of a triaxial ellipsoid:
The area of an ellipsoid with semi‐axes 3, 2, 1:
Use RegionMeasure to calculate the surface area of the ellipsoid:
Expectation value of the square root of a quadratic form over a normal distribution:
Compare to closed-form result in terms of CarlsonRG:
Text
Wolfram Research (2021), CarlsonRG, Wolfram Language function, https://reference.wolfram.com/language/ref/CarlsonRG.html.
CMS
Wolfram Language. 2021. "CarlsonRG." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CarlsonRG.html.
APA
Wolfram Language. (2021). CarlsonRG. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CarlsonRG.html