DLMF:9.8.E11 (Q2843): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10816 / rank
 
Normal rank
Property / Symbols used: Q10816 / qualifier
 
Defining formula:

arctan ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}

\atan@@{\NVar{z}}
Property / Symbols used: Q10816 / qualifier
 
xml-id: C4.S23.SS2.p1.m7abdec

Revision as of 14:39, 2 January 2020

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DLMF:9.8.E11
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    Statements

    Defining formula
    θ ⁡ ( x ) = 2 3 ⁢ π + arctan ⁡ ( Y 1 / 3 ⁡ ( ξ ) / J 1 / 3 ⁡ ( ξ ) ) , phase-Airy-Theta 𝑥 2 3 𝜋 Bessel-Y-Weber 1 3 𝜉 Bessel-J 1 3 𝜉 {\displaystyle{\displaystyle\theta\left(x\right)=\tfrac{2}{3}\pi+\operatorname% {arctan}\left(Y_{1/3}\left(\xi\right)/J_{1/3}\left(\xi\right)\right),}}
    0 references
    DLMF id
    DLMF:9.8.E11
    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.m2abdec
    0 references
    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.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q10816
    Defining formula
    arctan ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m7abdec
    0 references
     
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