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

- Mathematical function, suitable for both symbolic and numerical manipulation.
- For
,
and
,
.
- CarlsonRF[x,y,z] has a branch cut discontinuity for
.
- For certain arguments, CarlsonRF automatically evaluates to exact values.
- CarlsonRF can be evaluated to arbitrary numerical precision.
- CarlsonRF automatically threads over lists.
- CarlsonRF can be used with Interval and CenteredInterval objects. »
Examples
open allclose allBasic Examples (3)
Plot over a range of arguments:
CarlsonRF is related to Legendre elliptic integral of the first kind for
:
Scope (10)
Numerical Evaluation (6)
Precision of the output tracks the precision of the input:
Evaluate for complex arguments:
Evaluate efficiently at high precision:
CarlsonRF threads elementwise over lists:
CarlsonRF can be used with Interval and CenteredInterval objects:
Specific Values (2)
Function Representations (1)
TraditionalForm formatting:
Applications (3)
Distance along a meridian of the Earth:
Compare with the result of GeoDistance:
Expectation value of the reciprocal square root of a quadratic form over a normal distribution:
Compare with closed-form result in terms of CarlsonRF:
Express EllipticLog in terms of CarlsonRF:
Text
Wolfram Research (2021), CarlsonRF, Wolfram Language function, https://reference.wolfram.com/language/ref/CarlsonRF.html (updated 2023).
CMS
Wolfram Language. 2021. "CarlsonRF." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/CarlsonRF.html.
APA
Wolfram Language. (2021). CarlsonRF. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CarlsonRF.html