DLMF:10.47.E3 (Q3671)

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DLMF:10.47.E3
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    Statements

    Defining formula
    𝗃 n ⁡ ( z ) = 1 2 ⁢ π / z ⁢ J n + 1 2 ⁡ ( z ) = ( - 1 ) n ⁢ 1 2 ⁢ π / z ⁢ Y - n - 1 2 ⁡ ( z ) , spherical-Bessel-J 𝑛 𝑧 1 2 𝜋 𝑧 Bessel-J 𝑛 1 2 𝑧 superscript 1 𝑛 1 2 𝜋 𝑧 Bessel-Y-Weber 𝑛 1 2 𝑧 {\displaystyle{\displaystyle\mathsf{j}_{n}\left(z\right)=\sqrt{\tfrac{1}{2}\pi% /z}J_{n+\frac{1}{2}}\left(z\right)=(-1)^{n}\sqrt{\tfrac{1}{2}\pi/z}Y_{-n-\frac% {1}{2}}\left(z\right),}}
    0 references
    DLMF id
    DLMF:10.47.E3
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2adec
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    Bessel function of the second kind
    Defining formula
    Y ν ⁡ ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E3.m2adec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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    Q11429
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1bdec
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    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1bdec
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