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

- Mathematical function, suitable for both symbolic and numerical manipulation.
- For
and
,
.
- CarlsonRC[x,y] has a branch cut discontinuity at
.
- CarlsonRC[x,y] is real valued for
and
, being understood as a Cauchy principal value integral for
.
- For certain arguments, CarlsonRC automatically evaluates to exact values.
- CarlsonRC can be evaluated to arbitrary numerical precision.
- CarlsonRC automatically threads over lists.
Examples
open allclose allBasic Examples (3)
Scope (8)
Numerical Evaluation (5)
Precision of the output tracks the precision of the input:
Evaluate for complex arguments:
Evaluate efficiently at high precision:
CarlsonRC threads elementwise over lists:
Function Representations (1)
TraditionalForm formatting:
Applications (2)
Use CarlsonRC to provide an upper bound and lower bounds for CarlsonRF[x,y,z]:
CarlsonRC is useful for compactly expressing the change of parameter relations for EllipticPi:
Properties & Relations (2)
For , the
can be expressed in terms of ArcCos:
is interpreted as a principal value for
on the negative real axis:
Compare to the closed-form result in terms of positive arguments:
Text
Wolfram Research (2021), CarlsonRC, Wolfram Language function, https://reference.wolfram.com/language/ref/CarlsonRC.html.
CMS
Wolfram Language. 2021. "CarlsonRC." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CarlsonRC.html.
APA
Wolfram Language. (2021). CarlsonRC. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CarlsonRC.html