DLMF:7.7.E8 (Q2378): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
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 17:08, 30 December 2019

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DLMF:7.7.E8
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    Statements

    0 e - a 2 t 2 - ( b 2 / t 2 ) d t = π 2 a e - 2 a b , superscript subscript 0 superscript 𝑒 superscript 𝑎 2 superscript 𝑡 2 superscript 𝑏 2 superscript 𝑡 2 𝑡 𝜋 2 𝑎 superscript 𝑒 2 𝑎 𝑏 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-a^{2}t^{2}-(b^{2}/t^{2})}% \mathrm{d}t=\frac{\sqrt{\pi}}{2a}e^{-2ab},}}
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    DLMF:7.7.E8
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    | ph a | < 1 4 π phase 𝑎 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}a|<\tfrac{1}{4}\pi}}
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    | ph b | < 1 4 π phase 𝑏 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}b|<\tfrac{1}{4}\pi}}
    0 references