DLMF:19.33.E7 (Q6705): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aadec
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: Q11929 / rank
 
Normal rank
Property / Symbols used: Q11929 / qualifier
 
Defining formula:

L a subscript 𝐿 𝑎 {\displaystyle{\displaystyle L_{a}}}

L_{a}
Property / Symbols used: Q11929 / qualifier
 
xml-id: C19.S33.XMD10.m1dec
Property / Symbols used
 
Property / Symbols used: Q11930 / rank
 
Normal rank
Property / Symbols used: Q11930 / qualifier
 
Defining formula:

V 𝑉 {\displaystyle{\displaystyle V}}

V
Property / Symbols used: Q11930 / qualifier
 
xml-id: C19.S33.XMD6.m1dec

Latest revision as of 14:25, 2 January 2020

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DLMF:19.33.E7
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    Statements

    L c = 2 π a b c 0 d λ ( a 2 + λ ) ( b 2 + λ ) ( c 2 + λ ) 3 = V R D ( a 2 , b 2 , c 2 ) . subscript 𝐿 𝑐 2 𝜋 𝑎 𝑏 𝑐 superscript subscript 0 𝜆 superscript 𝑎 2 𝜆 superscript 𝑏 2 𝜆 superscript superscript 𝑐 2 𝜆 3 𝑉 Carlson-integral-RD superscript 𝑎 2 superscript 𝑏 2 superscript 𝑐 2 {\displaystyle{\displaystyle L_{c}=2\pi abc\int_{0}^{\infty}\frac{\mathrm{d}% \lambda}{\sqrt{(a^{2}+\lambda)(b^{2}+\lambda)(c^{2}+\lambda)^{3}}}=VR_{D}\left% (a^{2},b^{2},c^{2}\right).}}
    0 references
    DLMF:19.33.E7
    0 references
    R D ( x , y , z ) Carlson-integral-RD 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    C19.S16.E5.m2adec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1adec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3adec
    0 references
    L a subscript 𝐿 𝑎 {\displaystyle{\displaystyle L_{a}}}
    C19.S33.XMD10.m1dec
    0 references
    V 𝑉 {\displaystyle{\displaystyle V}}
    C19.S33.XMD6.m1dec
    0 references