DLMF:10.32.E5 (Q3525): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3addec

Revision as of 12:41, 2 January 2020

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DLMF:10.32.E5
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    Statements

    test
    K 0 ⁡ ( z ) = - 1 π ⁢ ∫ 0 π e ± z ⁢ cos ⁡ θ ⁢ ( γ + ln ⁡ ( 2 ⁢ z ⁢ ( sin ⁡ θ ) 2 ) ) ⁢ d θ . modified-Bessel-second-kind 0 𝑧 1 𝜋 superscript subscript 0 𝜋 superscript 𝑒 plus-or-minus 𝑧 𝜃 2 𝑧 superscript 𝜃 2 𝜃 {\displaystyle{\displaystyle K_{0}\left(z\right)=-\frac{1}{\pi}\int_{0}^{\pi}e% ^{\pm z\cos\theta}\left(\gamma+\ln\left(2z(\sin\theta)^{2}\right)\right)% \mathrm{d}\theta.}}
    0 references
    DLMF id
    DLMF:10.32.E5
    0 references
    Symbols used
    Euler’s constant
    test
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2addec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
     
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