DLMF:7.7.E12 (Q2382): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2akdec

Revision as of 01:45, 2 January 2020

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DLMF:7.7.E12
No description defined

    Statements

    Defining formula
    g ⁡ ( z ) + i ⁢ f ⁡ ( z ) = e - π ⁢ i ⁢ z 2 / 2 ⁢ ∫ z ∞ e π ⁢ i ⁢ t 2 / 2 ⁢ d t . Fresnel-auxilliary-function-g 𝑧 𝑖 Fresnel-auxilliary-function-f 𝑧 superscript 𝑒 𝜋 𝑖 superscript 𝑧 2 2 superscript subscript 𝑧 superscript 𝑒 𝜋 𝑖 superscript 𝑡 2 2 𝑡 {\displaystyle{\displaystyle\mathrm{g}\left(z\right)+i\mathrm{f}\left(z\right)% =e^{-\pi iz^{2}/2}\int_{z}^{\infty}e^{\pi it^{2}/2}\mathrm{d}t.}}
    0 references
    DLMF id
    DLMF:7.7.E12
    0 references
    Symbols used
    auxiliary function for Fresnel integrals
    Defining formula
    f ⁡ ( z ) Fresnel-auxilliary-function-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E10.m2aadec
    0 references
    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.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2akdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2akdec
    0 references
     
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