DLMF:19.29.E4 (Q6623): 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.m2adec
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.m1adec
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.m3adec
Property / Symbols used
 
Property / Symbols used: Q11899 / rank
 
Normal rank
Property / Symbols used: Q11899 / qualifier
 
Defining formula:

U n subscript 𝑈 𝑛 {\displaystyle{\displaystyle U_{n}}}

U_{n}
Property / Symbols used: Q11899 / qualifier
 
xml-id: C19.S29.XMD10.m1dec
Property / Symbols used
 
Property / Symbols used: Q11898 / rank
 
Normal rank
Property / Symbols used: Q11898 / qualifier
 
Defining formula:

s ⁢ ( t ) 𝑠 𝑡 {\displaystyle{\displaystyle s(t)}}

s(t)
Property / Symbols used: Q11898 / qualifier
 
xml-id: C19.S29.XMD4.m1adec

Latest revision as of 14:18, 2 January 2020

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DLMF:19.29.E4
No description defined

    Statements

    Defining formula
    ∫ y x d t s ⁢ ( t ) = 2 ⁢ R F ⁡ ( U 12 2 , U 13 2 , U 23 2 ) , superscript subscript 𝑦 𝑥 𝑡 𝑠 𝑡 2 Carlson-integral-RF superscript subscript 𝑈 12 2 superscript subscript 𝑈 13 2 superscript subscript 𝑈 23 2 {\displaystyle{\displaystyle\int_{y}^{x}\frac{\mathrm{d}t}{s(t)}=2R_{F}\left(U% _{12}^{2},U_{13}^{2},U_{23}^{2}\right),}}
    0 references
    DLMF id
    DLMF:19.29.E4
    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.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q11899
    Defining formula
    U n subscript 𝑈 𝑛 {\displaystyle{\displaystyle U_{n}}}
    xml-id
    C19.S29.XMD10.m1dec
    0 references
    Q11898
    Defining formula
    s ⁢ ( t ) 𝑠 𝑡 {\displaystyle{\displaystyle s(t)}}
    xml-id
    C19.S29.XMD4.m1adec
    0 references
     
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