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DLMF:10.47.E8 - MaRDI portal

DLMF:10.47.E8 (Q4373)

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DLMF:10.47.E8
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    Statements

    DLMF defining formula
    𝗂 n ( 2 ) ⁡ ( z ) = 1 2 ⁢ π / z ⁢ I - n - 1 2 ⁡ ( z ) spherical-Bessel-I-2 𝑛 𝑧 1 2 𝜋 𝑧 modified-Bessel-first-kind 𝑛 1 2 𝑧 {\displaystyle{\displaystyle{\mathsf{i}^{(2)}_{n}}\left(z\right)=\sqrt{\tfrac{% 1}{2}\pi/z}I_{-n-\frac{1}{2}}\left(z\right)}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    modified Bessel function of the first kind
    DLMF defining formula
    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
    integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1gdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1gdec
    0 references
     
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