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DLMF:10.24.E5 - MaRDI portal

DLMF:10.24.E5 (Q4179)

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DLMF:10.24.E5
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    Statements

    DLMF defining formula
    𝒲 ⁡ { J ~ ν ⁡ ( x ) , Y ~ ν ⁡ ( x ) } = 2 / ( π ⁢ x ) . Wronskian Bessel-J-imaginary-order 𝜈 𝑥 Bessel-Y-Weber-imaginary-order 𝜈 𝑥 2 𝜋 𝑥 {\displaystyle{\displaystyle\mathscr{W}\left\{\widetilde{J}_{\nu}\left(x\right% ),\widetilde{Y}_{\nu}\left(x\right)\right\}=2/(\pi x).}}
    0 references
    Symbols used
    Bessel function of imaginary order
    DLMF defining formula
    J ~ ν ⁡ ( x ) Bessel-J-imaginary-order 𝜈 𝑥 {\displaystyle{\displaystyle\widetilde{J}_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S24.Ex1.m2abdec
    0 references
    Bessel function of imaginary order
    DLMF defining formula
    Y ~ ν ⁡ ( x ) Bessel-Y-Weber-imaginary-order 𝜈 𝑥 {\displaystyle{\displaystyle\widetilde{Y}_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S24.Ex2.m2abdec
    0 references
    Wronskian
    DLMF defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3adec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1cdec
    0 references
    complex parameter
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1ddec
    0 references

    Identifiers

     
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