DLMF:19.29.E24 (Q6652): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: symmetric elliptic integral of first kind / rank
 
Normal rank
Property / Symbols used: symmetric elliptic integral of first kind / qualifier
 
Defining formula:

R F ( x , y , z ) Carlson-integral-RF 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}

\CarlsonsymellintRF@{\NVar{x}}{\NVar{y}}{\NVar{z}}
Property / Symbols used: symmetric elliptic integral of first kind / qualifier
 
xml-id: C19.S16.E1.m2acdec

Revision as of 14:21, 2 January 2020

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DLMF:19.29.E24
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    Statements

    y x d t Q 1 ( t ) Q 2 ( t ) = 4 R F ( U , U + D 12 + V , U + D 12 - V ) , superscript subscript 𝑦 𝑥 𝑡 subscript 𝑄 1 𝑡 subscript 𝑄 2 𝑡 4 Carlson-integral-RF 𝑈 𝑈 subscript 𝐷 12 𝑉 𝑈 subscript 𝐷 12 𝑉 {\displaystyle{\displaystyle\int_{y}^{x}\frac{\mathrm{d}t}{\sqrt{Q_{1}(t)Q_{2}% (t)}}=4R_{F}\left(U,U+D_{12}+V,U+D_{12}-V\right),}}
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    DLMF:19.29.E24
    0 references
    R F ( x , y , z ) Carlson-integral-RF 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    C19.S16.E1.m2acdec
    0 references