DLMF:10.32.E3 (Q3523): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11429 / rank
 
Normal rank
Property / Symbols used: Q11429 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11429 / qualifier
 
xml-id: C10.S1.XMD2.m1dec

Revision as of 13:40, 2 January 2020

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DLMF:10.32.E3
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    Statements

    test
    I n ⁡ ( z ) = 1 π ⁢ ∫ 0 π e z ⁢ cos ⁡ θ ⁢ cos ⁡ ( n ⁢ θ ) ⁢ d θ . modified-Bessel-first-kind 𝑛 𝑧 1 𝜋 superscript subscript 0 𝜋 superscript 𝑒 𝑧 𝜃 𝑛 𝜃 𝜃 {\displaystyle{\displaystyle I_{n}\left(z\right)=\frac{1}{\pi}\int_{0}^{\pi}e^% {z\cos\theta}\cos\left(n\theta\right)\mathrm{d}\theta.}}
    0 references
    DLMF id
    DLMF:10.32.E3
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    modified Bessel function of the first kind
    test
    I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E2.m2abdec
    0 references
    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1dec
    0 references
     
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