DLMF:10.9.E3 (Q3068): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2abdec

Revision as of 15:11, 2 January 2020

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DLMF:10.9.E3
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    Statements

    Defining formula
    Y 0 ⁡ ( z ) = 4 π 2 ⁢ ∫ 0 1 2 ⁢ π cos ⁡ ( z ⁢ cos ⁡ θ ) ⁢ ( γ + ln ⁡ ( 2 ⁢ z ⁢ sin 2 ⁡ θ ) ) ⁢ d θ , Bessel-Y-Weber 0 𝑧 4 superscript 𝜋 2 superscript subscript 0 1 2 𝜋 𝑧 𝜃 2 𝑧 2 𝜃 𝜃 {\displaystyle{\displaystyle Y_{0}\left(z\right)=\frac{4}{\pi^{2}}\int_{0}^{% \frac{1}{2}\pi}\cos\left(z\cos\theta\right)\left(\gamma+\ln\left(2z{\sin^{2}}% \theta\right)\right)\mathrm{d}\theta,}}
    0 references
    DLMF id
    DLMF:10.9.E3
    0 references
    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.m2adec
    0 references
    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.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.m2abdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2abdec
    0 references
     
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