DLMF:7.7.E4 (Q2374): 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.m2acdec

Revision as of 01:43, 2 January 2020

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DLMF:7.7.E4
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    Statements

    Defining formula
    ∫ 0 ∞ e - a ⁢ t t + z 2 ⁢ d t = π a ⁢ e a ⁢ z 2 ⁢ erfc ⁡ ( a ⁢ z ) , superscript subscript 0 superscript 𝑒 𝑎 𝑡 𝑡 superscript 𝑧 2 𝑡 𝜋 𝑎 superscript 𝑒 𝑎 superscript 𝑧 2 complementary-error-function 𝑎 𝑧 {\displaystyle{\displaystyle\int_{0}^{\infty}\frac{e^{-at}}{\sqrt{t+z^{2}}}% \mathrm{d}t=\sqrt{\frac{\pi}{a}}e^{az^{2}}\operatorname{erfc}\left(\sqrt{a}z% \right),}}
    0 references
    DLMF id
    DLMF:7.7.E4
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    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
    0 references
    ℜ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
     
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