DLMF:10.45.E4 (Q3660)

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DLMF:10.45.E4
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    Statements

    Defining formula
    𝒲 ⁡ { K ~ ν ⁡ ( x ) , I ~ ν ⁡ ( x ) } = 1 / x . Wronskian modified-Bessel-second-kind-imaginary-order 𝜈 𝑥 modified-Bessel-first-kind-imaginary-order 𝜈 𝑥 1 𝑥 {\displaystyle{\displaystyle\mathscr{W}\left\{\widetilde{K}_{\nu}\left(x\right% ),\widetilde{I}_{\nu}\left(x\right)\right\}=1/x.}}
    0 references
    DLMF id
    DLMF:10.45.E4
    0 references
    Symbols used
    Q10865
    Defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3adec
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    modified Bessel function of the first kind of imaginary order
    Defining formula
    I ~ ν ⁡ ( x ) modified-Bessel-first-kind-imaginary-order 𝜈 𝑥 {\displaystyle{\displaystyle\widetilde{I}_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S45.E2.m2abdec
    0 references
    modified Bessel function fo the second kind of imaginary order
    Defining formula
    K ~ ν ⁡ ( x ) modified-Bessel-second-kind-imaginary-order 𝜈 𝑥 {\displaystyle{\displaystyle\widetilde{K}_{\NVar{\nu}}\left(\NVar{x}\right)}}
    xml-id
    C10.S45.E2.m3abdec
    0 references
    Q11435
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1cdec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1cdec
    0 references
     
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