DLMF:19.34.E1 (Q6711): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11906 / rank
 
Normal rank
Property / Symbols used: Q11906 / qualifier
 
Defining formula:

I ⁢ ( 𝐦 ) 𝐼 𝐦 {\displaystyle{\displaystyle I(\mathbf{m})}}

I(\mathbf{m})
Property / Symbols used: Q11906 / qualifier
 
xml-id: C19.S29.XMD13.m1dec

Revision as of 14:26, 2 January 2020

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DLMF:19.34.E1
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    Statements

    Defining formula
    c 2 ⁢ M 2 ⁢ π = a ⁢ b ⁢ ∫ 0 2 ⁢ π ( h 2 + a 2 + b 2 - 2 ⁢ a ⁢ b ⁢ cos ⁡ θ ) - 1 / 2 ⁢ cos ⁡ θ ⁢ d θ = 2 ⁢ a ⁢ b ⁢ ∫ - 1 1 t ⁢ d t ( 1 + t ) ⁢ ( 1 - t ) ⁢ ( a 3 - 2 ⁢ a ⁢ b ⁢ t ) = 2 ⁢ a ⁢ b ⁢ I ⁢ ( 𝐞 5 ) , speed-of-light 2 𝑀 2 𝜋 𝑎 𝑏 superscript subscript 0 2 𝜋 superscript superscript ℎ 2 superscript 𝑎 2 superscript 𝑏 2 2 𝑎 𝑏 𝜃 1 2 𝜃 𝜃 2 𝑎 𝑏 superscript subscript 1 1 𝑡 𝑡 1 𝑡 1 𝑡 subscript 𝑎 3 2 𝑎 𝑏 𝑡 2 𝑎 𝑏 𝐼 subscript 𝐞 5 {\displaystyle{\displaystyle\frac{{c^{2}}M}{2\pi}=ab\int_{0}^{2\pi}(h^{2}+a^{2% }+b^{2}-2ab\cos\theta)^{-1/2}\cos\theta\mathrm{d}\theta=2ab\int_{-1}^{1}\frac{% t\mathrm{d}t}{\sqrt{(1+t)(1-t)(a_{3}-2abt)}}=2abI(\mathbf{e}_{5}),}}
    0 references
    DLMF id
    DLMF:19.34.E1
    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.m1adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q11906
    Defining formula
    I ⁢ ( 𝐦 ) 𝐼 𝐦 {\displaystyle{\displaystyle I(\mathbf{m})}}
    xml-id
    C19.S29.XMD13.m1dec
    0 references
     
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