Formula:7124

Digital Library of Mathematical Functions ID 19.21.E10

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle 2\CarlsonsymellintRG@{x}{y}{z}=z\CarlsonsymellintRF@{x}{y}{z}-\tfrac{1}{3}(x-z)(y-z)\CarlsonsymellintRD@{x}{y}{z}+\sqrt{xy/z},}

Constraint(s)

${\displaystyle{\displaystyle z\neq 0}}$

Symbols List

• ${\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: elliptic integral symmetric in only two variables
• ${\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: symmetric elliptic integral of first kind
• ${\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}$: symmetric elliptic integral of second kind
 

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