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## Carlson's Elliptic Integrals

This tool evaluates the Carlson's symmetric form of elliptic integrals: R_{F}(x,y,z), R_{C}(x,y), R_{D}(x,y,z) and R_{J}(x,y,z,p). Arguments x, y, z should be generally non-negative, but more restrictions apply. Argument p should be non-zero. Enter the arguments below.

x = | |||

y = | |||

z = | |||

p = | |||

Result: | |||

R _{F }(x,y,z) = | |||

R _{C }(x,y) = | |||

R _{D }(x,y,z) = | |||

R _{J }(x,y,z,p) = |

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## About Carlson's symmetric form of Elliptic Integrals

### Definitions

The Carlson's symmetric form of the elliptic integral of the first kind is defined as:

The Carlson's degenerate elliptic integral of the first kind, with y=z, is defined as:

The Carlson's symmetric form of the elliptic integral of the second kind is defined as:

The Carlson's symmetric form of the elliptic integral of the third kind is defined as: