DLMF:7.7.E3 (Q2373): Difference between revisions

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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
 
test:

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.m2abdec

Revision as of 00:43, 2 January 2020

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DLMF:7.7.E3
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    Statements

    test
    ∫ 0 ∞ e - a ⁢ t 2 + 2 ⁢ i ⁢ z ⁢ t ⁢ d t = 1 2 ⁢ π a ⁢ e - z 2 / a + i a ⁢ F ⁡ ( z a ) , superscript subscript 0 superscript 𝑒 𝑎 superscript 𝑡 2 2 𝑖 𝑧 𝑡 𝑡 1 2 𝜋 𝑎 superscript 𝑒 superscript 𝑧 2 𝑎 𝑖 𝑎 Dawsons-integral 𝑧 𝑎 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at^{2}+2izt}\mathrm{d}t=\frac% {1}{2}\sqrt{\frac{\pi}{a}}e^{-z^{2}/a}+\frac{i}{\sqrt{a}}F\left(\frac{z}{\sqrt% {a}}\right),}}
    0 references
    DLMF id
    DLMF:7.7.E3
    0 references
    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
    0 references
    Symbols used
    Dawson’s integral
    test
    F ⁡ ( z ) Dawsons-integral 𝑧 {\displaystyle{\displaystyle F\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E5.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
     
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