DLMF:12.14.E28 (Q4268): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: function (locally) / rank
 
Normal rank
Property / Symbols used: function (locally) / qualifier
 
Defining formula:

ϕ ⁢ ( ζ ) italic-ϕ 𝜁 {\displaystyle{\displaystyle\phi(\zeta)}}

\phi(\zeta)
Property / Symbols used: function (locally) / qualifier
 
xml-id: C12.S10.XMD22.m1dec

Revision as of 15:31, 2 January 2020

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DLMF:12.14.E28
No description defined

    Statements

    Defining formula
    l ⁢ ( μ ) = 2 ⁢ e 1 8 ⁢ π ⁢ μ 2 ⁢ e i ⁢ ( 1 2 ⁢ ϕ 2 - 1 8 ⁢ π ) ⁢ g ⁢ ( μ ⁢ e - 1 4 ⁢ π ⁢ i ) , 𝑙 𝜇 2 superscript 𝑒 1 8 𝜋 superscript 𝜇 2 superscript 𝑒 𝑖 1 2 subscript italic-ϕ 2 1 8 𝜋 𝑔 𝜇 superscript 𝑒 1 4 𝜋 𝑖 {\displaystyle{\displaystyle l(\mu)=\sqrt{2}e^{\frac{1}{8}\pi\mu^{2}}e^{i(% \frac{1}{2}\phi_{2}-\frac{1}{8}\pi)}g(\mu e^{-\frac{1}{4}\pi i}),}}
    0 references
    DLMF id
    DLMF:12.14.E28
    0 references
    comment
    Warning: Falling back to standard tex;
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aidec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ahdec
    0 references
    function (locally)
    Defining formula
    ϕ ⁢ ( ζ ) italic-ϕ 𝜁 {\displaystyle{\displaystyle\phi(\zeta)}}
    xml-id
    C12.S10.XMD22.m1dec
    0 references
     
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