DLMF:10.32.E15 (Q3535)

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DLMF:10.32.E15
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    Statements

    test
    I μ ⁡ ( z ) ⁢ I ν ⁡ ( z ) = 2 π ⁢ ∫ 0 1 2 ⁢ π I μ + ν ⁡ ( 2 ⁢ z ⁢ cos ⁡ θ ) ⁢ cos ⁡ ( ( μ - ν ) ⁢ θ ) ⁢ d θ , modified-Bessel-first-kind 𝜇 𝑧 modified-Bessel-first-kind 𝜈 𝑧 2 𝜋 superscript subscript 0 1 2 𝜋 modified-Bessel-first-kind 𝜇 𝜈 2 𝑧 𝜃 𝜇 𝜈 𝜃 𝜃 {\displaystyle{\displaystyle I_{\mu}\left(z\right)I_{\nu}\left(z\right)=\frac{% 2}{\pi}\int_{0}^{\frac{1}{2}\pi}I_{\mu+\nu}\left(2z\cos\theta\right)\cos\left(% (\mu-\nu)\theta\right)\mathrm{d}\theta,}}
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    DLMF id
    DLMF:10.32.E15
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    constraint
    ℜ ⁡ ( μ + ν ) > - 1 𝜇 𝜈 1 {\displaystyle{\displaystyle\Re(\mu+\nu)>-1}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2amdec
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    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aidec
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    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1andec
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