DLMF:10.57.E1 (Q3770)

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DLMF:10.57.E1
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    Statements

    Defining formula
    𝗃 n ′ ⁡ ( ( n + 1 2 ) ⁢ z ) = π 1 2 ( ( 2 ⁢ n + 1 ) ⁢ z ) 1 2 ⁢ J n + 1 2 ′ ⁡ ( ( n + 1 2 ) ⁢ z ) - π 1 2 ( ( 2 ⁢ n + 1 ) ⁢ z ) 3 2 ⁢ J n + 1 2 ⁡ ( ( n + 1 2 ) ⁢ z ) . diffop spherical-Bessel-J 𝑛 1 𝑛 1 2 𝑧 superscript 𝜋 1 2 superscript 2 𝑛 1 𝑧 1 2 diffop Bessel-J 𝑛 1 2 1 𝑛 1 2 𝑧 superscript 𝜋 1 2 superscript 2 𝑛 1 𝑧 3 2 Bessel-J 𝑛 1 2 𝑛 1 2 𝑧 {\displaystyle{\displaystyle\mathsf{j}_{n}'\left((n+\tfrac{1}{2})z\right)=% \frac{\pi^{\frac{1}{2}}}{((2n+1)z)^{\frac{1}{2}}}J_{n+\frac{1}{2}}'\left((n+% \tfrac{1}{2})z\right)-\frac{\pi^{\frac{1}{2}}}{((2n+1)z)^{\frac{3}{2}}}J_{n+% \frac{1}{2}}\left((n+\tfrac{1}{2})z\right).}}
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    DLMF id
    DLMF:10.57.E1
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    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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    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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    spherical Bessel function of the first kind
    Defining formula
    𝗃 n ⁡ ( z ) spherical-Bessel-J 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E3.m2adec
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    Q11429
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1dec
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    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1dec
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