DLMF:11.10.E36 (Q4058)

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DLMF:11.10.E36
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    Statements

    Defining formula
    z ⁢ 𝐉 ν ′ ⁡ ( z ) ± ν ⁢ 𝐉 ν ⁡ ( z ) = ± z ⁢ 𝐉 ν ∓ 1 ⁡ ( z ) ± sin ⁡ ( π ⁢ ν ) π , plus-or-minus 𝑧 diffop Anger-J 𝜈 1 𝑧 𝜈 Anger-J 𝜈 𝑧 plus-or-minus plus-or-minus 𝑧 Anger-J minus-or-plus 𝜈 1 𝑧 𝜋 𝜈 𝜋 {\displaystyle{\displaystyle z\mathbf{J}_{\nu}'\left(z\right)\pm\nu\mathbf{J}_% {\nu}\left(z\right)=\pm z\mathbf{J}_{\nu\mp 1}\left(z\right)\pm\frac{\sin\left% (\pi\nu\right)}{\pi},}}
    0 references
    DLMF id
    DLMF:11.10.E36
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    Symbols used
    Anger function
    Defining formula
    𝐉 ν ⁡ ( z ) Anger-J 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{J}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E1.m2asdec
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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.m2aaadec
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