DLMF:10.27.E2 (Q3492)

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DLMF:10.27.E2
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    Statements

    test
    I - ν ⁡ ( z ) = I ν ⁡ ( z ) + ( 2 / π ) ⁢ sin ⁡ ( ν ⁢ π ) ⁢ K ν ⁡ ( z ) , modified-Bessel-first-kind 𝜈 𝑧 modified-Bessel-first-kind 𝜈 𝑧 2 𝜋 𝜈 𝜋 modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{-\nu}\left(z\right)=I_{\nu}\left(z\right)+(2/% \pi)\sin\left(\nu\pi\right)K_{\nu}\left(z\right),}}
    0 references
    DLMF id
    DLMF:10.27.E2
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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.m2adec
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    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.m2aadec
    0 references
     
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