DLMF:11.10.E15 (Q4033)

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DLMF:11.10.E15
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    Statements

    Defining formula
    𝐉 Ξ½ ⁑ ( z ) = J Ξ½ ⁑ ( z ) + sin ⁑ ( Ο€ ⁒ Ξ½ ) ⁒ 𝐀 Ξ½ ⁑ ( z ) , Anger-J 𝜈 𝑧 Bessel-J 𝜈 𝑧 πœ‹ 𝜈 associated-Anger-Weber-A 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{J}_{\nu}\left(z\right)=J_{\nu}\left(z% \right)+\sin\left(\pi\nu\right)\,\mathbf{A}_{\nu}\left(z\right),}}
    0 references
    DLMF id
    DLMF:11.10.E15
    0 references
    Symbols used
    Anger function
    Defining formula
    𝐉 Ξ½ ⁑ ( z ) Anger-J 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{J}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E1.m2aidec
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    Bessel function of the first kind
    Defining formula
    J Ξ½ ⁑ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2adec
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    Anger–Weber function
    Defining formula
    𝐀 Ξ½ ⁑ ( z ) associated-Anger-Weber-A 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{A}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E4.m2aadec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    Ο€ {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ajdec
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    sine function
    Defining formula
    sin ⁑ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2ahdec
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    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1ndec
    0 references
    Q11492
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1rdec
    0 references
     
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