DLMF:7.14.E1 (Q2433): Difference between revisions

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Property / constraint
 

| ph ⁡ b | < 1 4 ⁢ π phase 𝑏 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}b|<\tfrac{1}{4}\pi}}

|\phase@@{b}|<\tfrac{1}{4}\pi
Property / constraint: | ph ⁡ b | < 1 4 ⁢ π phase 𝑏 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}b|<\tfrac{1}{4}\pi}} / rank
 
Normal rank

Revision as of 16:08, 30 December 2019

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DLMF:7.14.E1
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    Statements

    test
    ∫ 0 ∞ e 2 ⁢ i ⁢ a ⁢ t ⁢ erfc ⁡ ( b ⁢ t ) ⁢ d t = 1 a ⁢ π ⁢ F ⁡ ( a b ) + i 2 ⁢ a ⁢ ( 1 - e - ( a / b ) 2 ) , superscript subscript 0 superscript 𝑒 2 𝑖 𝑎 𝑡 complementary-error-function 𝑏 𝑡 𝑡 1 𝑎 𝜋 Dawsons-integral 𝑎 𝑏 𝑖 2 𝑎 1 superscript 𝑒 superscript 𝑎 𝑏 2 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{2iat}\operatorname{erfc}\left(% bt\right)\mathrm{d}t={\frac{1}{a\sqrt{\pi}}F\left(\frac{a}{b}\right)+\frac{i}{% 2a}\left(1-e^{-(a/b)^{2}}\right)},}}
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    DLMF id
    DLMF:7.14.E1
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    constraint
    a ∈ ℂ 𝑎 {\displaystyle{\displaystyle a\in\mathbb{C}}}
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    | ph ⁡ b | < 1 4 ⁢ π phase 𝑏 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}b|<\tfrac{1}{4}\pi}}
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