DLMF:10.23.E16 (Q3470)

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DLMF:10.23.E16
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    Statements

    Defining formula
    Y 0 ⁡ ( z ) = 2 π ⁢ ( ln ⁡ ( 1 2 ⁢ z ) + γ ) ⁢ J 0 ⁡ ( z ) - 4 π ⁢ ∑ k = 1 ∞ ( - 1 ) k ⁢ J 2 ⁢ k ⁡ ( z ) k , Bessel-Y-Weber 0 𝑧 2 𝜋 1 2 𝑧 Bessel-J 0 𝑧 4 𝜋 superscript subscript 𝑘 1 superscript 1 𝑘 Bessel-J 2 𝑘 𝑧 𝑘 {\displaystyle{\displaystyle Y_{0}\left(z\right)=\frac{2}{\pi}\left(\ln\left(% \tfrac{1}{2}z\right)+\gamma\right)J_{0}\left(z\right)-\frac{4}{\pi}\sum_{k=1}^% {\infty}(-1)^{k}\frac{J_{2k}\left(z\right)}{k},}}
    0 references
    DLMF id
    DLMF:10.23.E16
    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.m2akdec
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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
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    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2adec
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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.m2aadec
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    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    Q11428
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1ndec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1idec
    0 references
     
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