DLMF:10.27.E11 (Q3501)

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DLMF:10.27.E11
No description defined

    Statements

    Defining formula
    Y ν ⁡ ( z ) = e ± ( ν + 1 ) ⁢ π ⁢ i / 2 ⁢ I ν ⁡ ( z ⁢ e ∓ π ⁢ i / 2 ) - ( 2 / π ) ⁢ e ∓ ν ⁢ π ⁢ i / 2 ⁢ K ν ⁡ ( z ⁢ e ∓ π ⁢ i / 2 ) , Bessel-Y-Weber 𝜈 𝑧 superscript 𝑒 plus-or-minus 𝜈 1 𝜋 𝑖 2 modified-Bessel-first-kind 𝜈 𝑧 superscript 𝑒 minus-or-plus 𝜋 𝑖 2 2 𝜋 superscript 𝑒 minus-or-plus 𝜈 𝜋 𝑖 2 modified-Bessel-second-kind 𝜈 𝑧 superscript 𝑒 minus-or-plus 𝜋 𝑖 2 {\displaystyle{\displaystyle Y_{\nu}\left(z\right)=e^{\pm(\nu+1)\pi i/2}I_{\nu% }\left(ze^{\mp\pi i/2}\right)-(2/\pi)e^{\mp\nu\pi i/2}K_{\nu}\left(ze^{\mp\pi i% /2}\right),}}
    0 references
    DLMF id
    DLMF:10.27.E11
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    constraint
    - 1 2 ⁢ π ≤ ± ph ⁡ z ≤ π 1 2 𝜋 plus-or-minus phase 𝑧 𝜋 {\displaystyle{\displaystyle-\tfrac{1}{2}\pi\leq\pm\operatorname{ph}z\leq\pi}}
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    Symbols used
    Bessel function of the second kind
    Defining formula
    Y ν ⁡ ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E3.m2aadec
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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.m2agdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aedec
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    modified Bessel function of the first kind
    Defining formula
    I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E2.m2afdec
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    modified Bessel function of the second kind
    Defining formula
    K ν ⁡ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E3.m2agdec
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    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1aedec
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    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1jdec
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    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1idec
    0 references
     
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