DLMF:19.16.E3 (Q6318): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2adec

Revision as of 13:52, 2 January 2020

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DLMF:19.16.E3
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    Statements

    Defining formula
    R G ⁡ ( x , y , z ) = 1 4 ⁢ π ⁢ ∫ 0 2 ⁢ π ∫ 0 π ( x ⁢ sin 2 ⁡ θ ⁢ cos 2 ⁡ ϕ + y ⁢ sin 2 ⁡ θ ⁢ sin 2 ⁡ ϕ + z ⁢ cos 2 ⁡ θ ) 1 2 ⁢ sin ⁡ θ ⁢ d θ ⁢ d ϕ , Carlson-integral-RG 𝑥 𝑦 𝑧 1 4 𝜋 superscript subscript 0 2 𝜋 superscript subscript 0 𝜋 superscript 𝑥 2 𝜃 2 italic-ϕ 𝑦 2 𝜃 2 italic-ϕ 𝑧 2 𝜃 1 2 𝜃 𝜃 italic-ϕ {\displaystyle{\displaystyle R_{G}\left(x,y,z\right)=\frac{1}{4\pi}\int_{0}^{2% \pi}\!\!\!\!\int_{0}^{\pi}\left(x{\sin^{2}}\theta{\cos^{2}}\phi+y{\sin^{2}}% \theta{\sin^{2}}\phi+z{\cos^{2}}\theta\right)^{\frac{1}{2}}\sin\theta\mathrm{d% }\theta\mathrm{d}\phi,}}
    0 references
    DLMF id
    DLMF:19.16.E3
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
     
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