DLMF:19.23.E2 (Q6473): Difference between revisions

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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.m1aadec

Revision as of 14:01, 2 January 2020

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DLMF:19.23.E2
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    Statements

    Defining formula
    R G ⁡ ( 0 , y , z ) = 1 2 ⁢ ∫ 0 π / 2 ( y ⁢ cos 2 ⁡ θ + z ⁢ sin 2 ⁡ θ ) 1 / 2 ⁢ d θ , Carlson-integral-RG 0 𝑦 𝑧 1 2 superscript subscript 0 𝜋 2 superscript 𝑦 2 𝜃 𝑧 2 𝜃 1 2 𝜃 {\displaystyle{\displaystyle R_{G}\left(0,y,z\right)=\frac{1}{2}\int_{0}^{\pi/% 2}(y{\cos^{2}}\theta+z{\sin^{2}}\theta)^{1/2}\mathrm{d}\theta,}}
    0 references
    DLMF id
    DLMF:19.23.E2
    0 references
    Symbols used
    symmetric elliptic integral of second kind
    Defining formula
    R G ⁡ ( x , y , z ) Carlson-integral-RG 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E3.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
     
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