CarlsonRM

CarlsonRM[x,y,ρ]

gives Carlson's elliptic integral .

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • For non-negative arguments, .
  • CarlsonRM[x,y,ρ] has a branch cut discontinuity at .
  • CarlsonRM[x,y,ρ] is understood as a Cauchy principal value integral for ρ<0.
  • For certain arguments, CarlsonRM automatically evaluates to exact values.
  • CarlsonRM can be evaluated to arbitrary precision.
  • CarlsonRM automatically threads over lists.

Examples

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Basic Examples  (3)

Evaluate numerically:

Plot the function:

CarlsonRM is related to complete Legendre elliptic integral of the third kind:

Scope  (8)

Numerical Evaluation  (5)

Evaluate numerically:

Evaluate numerically to high precision:

Precision of the output tracks the precision of the input:

Evaluate for complex arguments:

Evaluate efficiently at high precision:

CarlsonRM threads elementwise over lists:

Specific Values  (1)

Simple exact values are generated automatically:

Derivatives  (1)

Derivative of TemplateBox[{x, y, z}, CarlsonRM] with respect to :

Derivative of TemplateBox[{x, y, z}, CarlsonRM] with respect to :

Function Representations  (1)

TraditionalForm formatting:

Applications  (2)

Visualize the solid angle subtended by a circular disk:

Evaluate the solid angle:

Compare with the result of NIntegrate:

Visualize the intersection of a cylinder and a ball:

Volume of cylinder-ball intersection expressed in terms of Carlson integrals:

Compare with the result of Volume:

Wolfram Research (2021), CarlsonRM, Wolfram Language function, https://reference.wolfram.com/language/ref/CarlsonRM.html.

Text

Wolfram Research (2021), CarlsonRM, Wolfram Language function, https://reference.wolfram.com/language/ref/CarlsonRM.html.

BibTeX

@misc{reference.wolfram_2021_carlsonrm, author="Wolfram Research", title="{CarlsonRM}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/CarlsonRM.html}", note=[Accessed: 26-September-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_carlsonrm, organization={Wolfram Research}, title={CarlsonRM}, year={2021}, url={https://reference.wolfram.com/language/ref/CarlsonRM.html}, note=[Accessed: 26-September-2021 ]}

CMS

Wolfram Language. 2021. "CarlsonRM." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CarlsonRM.html.

APA

Wolfram Language. (2021). CarlsonRM. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CarlsonRM.html