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
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1aidec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aidec
Property / Symbols used
 
Property / Symbols used: Q11908 / rank
 
Normal rank
Property / Symbols used: Q11908 / qualifier
 
Defining formula:

U 𝑈 {\displaystyle{\displaystyle U}}

U
Property / Symbols used: Q11908 / qualifier
 
xml-id: C19.S29.XMD16.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11910 / rank
 
Normal rank
Property / Symbols used: Q11910 / qualifier
 
Defining formula:

D j ⁢ l subscript 𝐷 𝑗 𝑙 {\displaystyle{\displaystyle D_{jl}}}

D_{jl}
Property / Symbols used: Q11910 / qualifier
 
xml-id: C19.S29.XMD21.m1dec
Property / Symbols used
 
Property / Symbols used: Q11911 / rank
 
Normal rank
Property / Symbols used: Q11911 / qualifier
 
Defining formula:

V 𝑉 {\displaystyle{\displaystyle V}}

V
Property / Symbols used: Q11911 / qualifier
 
xml-id: C19.S29.XMD23.m1dec
Property / Symbols used
 
Property / Symbols used: Q11909 / rank
 
Normal rank
Property / Symbols used: Q11909 / qualifier
 
Defining formula:

Q ⁢ ( t 2 ) 𝑄 superscript 𝑡 2 {\displaystyle{\displaystyle Q(t^{2})}}

Q(t^{2})
Property / Symbols used: Q11909 / qualifier
 
xml-id: C19.S29.XMD24.m1ddec

Latest revision as of 14:21, 2 January 2020

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DLMF:19.29.E24
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    Statements

    Defining formula
    ∫ 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),}}
    0 references
    DLMF id
    DLMF:19.29.E24
    0 references
    Symbols used
    symmetric elliptic integral of first kind
    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)}}
    xml-id
    C19.S16.E1.m2acdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aidec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aidec
    0 references
    Q11908
    Defining formula
    U 𝑈 {\displaystyle{\displaystyle U}}
    xml-id
    C19.S29.XMD16.m1ddec
    0 references
    Q11910
    Defining formula
    D j ⁢ l subscript 𝐷 𝑗 𝑙 {\displaystyle{\displaystyle D_{jl}}}
    xml-id
    C19.S29.XMD21.m1dec
    0 references
    Q11911
    Defining formula
    V 𝑉 {\displaystyle{\displaystyle V}}
    xml-id
    C19.S29.XMD23.m1dec
    0 references
    Q11909
    Defining formula
    Q ⁢ ( t 2 ) 𝑄 superscript 𝑡 2 {\displaystyle{\displaystyle Q(t^{2})}}
    xml-id
    C19.S29.XMD24.m1ddec
    0 references
     
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