DLMF:10.23.E16 (Q3470): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aadec

Revision as of 12:32, 2 January 2020

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DLMF:10.23.E16
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    Statements

    test
    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
    test
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2akdec
    0 references
    Bessel function of the second kind
    test
    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
    Euler’s constant
    test
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
     
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