DLMF:7.7.E15 (Q2385): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2andec

Revision as of 01:46, 2 January 2020

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DLMF:7.7.E15
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    Statements

    Defining formula
    ∫ 0 ∞ e - a ⁢ t ⁢ cos ⁡ ( t 2 ) ⁢ d t = π 2 ⁢ f ⁡ ( a 2 ⁢ π ) , superscript subscript 0 superscript 𝑒 𝑎 𝑡 superscript 𝑡 2 𝑡 𝜋 2 Fresnel-auxilliary-function-f 𝑎 2 𝜋 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}\cos\left(t^{2}\right)% \mathrm{d}t=\sqrt{\frac{\pi}{2}}\mathrm{f}\left(\frac{a}{\sqrt{2\pi}}\right),}}
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    DLMF id
    DLMF:7.7.E15
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    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
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    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.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2andec
    0 references
     
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