DLMF:10.11.E2 (Q3104)

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DLMF:10.11.E2
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    Statements

    Defining formula
    Y ν ⁡ ( z ⁢ e m ⁢ π ⁢ i ) = e - m ⁢ ν ⁢ π ⁢ i ⁢ Y ν ⁡ ( z ) + 2 ⁢ i ⁢ sin ⁡ ( m ⁢ ν ⁢ π ) ⁢ cot ⁡ ( ν ⁢ π ) ⁢ J ν ⁡ ( z ) . Bessel-Y-Weber 𝜈 𝑧 superscript 𝑒 𝑚 𝜋 𝑖 superscript 𝑒 𝑚 𝜈 𝜋 𝑖 Bessel-Y-Weber 𝜈 𝑧 2 𝑖 𝑚 𝜈 𝜋 𝜈 𝜋 Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\nu}\left(ze^{m\pi i}\right)=e^{-m\nu\pi i}Y_{% \nu}\left(z\right)+2i\sin\left(m\nu\pi\right)\cot\left(\nu\pi\right)J_{\nu}% \left(z\right).}}
    0 references
    DLMF id
    DLMF:10.11.E2
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2aadec
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    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.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    cotangent function
    Defining formula
    cot ⁡ z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}
    xml-id
    C4.S14.E7.m2adec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
    Q11438
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C10.S1.XMD1.m1adec
    0 references
     
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