DLMF:7.14.E6 (Q2438): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: auxiliary function for Fresnel integrals / rank
 
Normal rank
Property / Symbols used: auxiliary function for Fresnel integrals / qualifier
 
Defining formula:

g ⁡ ( z ) Fresnel-auxilliary-function-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}

\auxFresnelg@{\NVar{z}}
Property / Symbols used: auxiliary function for Fresnel integrals / qualifier
 
xml-id: C7.S2.E11.m2adec

Revision as of 01:52, 2 January 2020

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DLMF:7.14.E6
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    Statements

    Defining formula
    ∫ 0 ∞ e - a ⁢ t ⁢ S ⁡ ( t ) ⁢ d t = 1 a ⁢ g ⁡ ( a π ) , superscript subscript 0 superscript 𝑒 𝑎 𝑡 Fresnel-sine-integral 𝑡 𝑡 1 𝑎 Fresnel-auxilliary-function-g 𝑎 𝜋 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}S\left(t\right)\mathrm{d}t% =\frac{1}{a}\mathrm{g}\left(\frac{a}{\pi}\right),}}
    0 references
    DLMF id
    DLMF:7.14.E6
    0 references
    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
    0 references
    Symbols used
    auxiliary function for Fresnel integrals
    Defining formula
    g ⁡ ( z ) Fresnel-auxilliary-function-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E11.m2adec
    0 references
     
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