DLMF:4.40.E9 (Q1981): Difference between revisions

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Property / constraint
 

- 1 < a < 1 1 𝑎 1 {\displaystyle{\displaystyle-1<a<1}}

-1<a<1
Property / constraint: - 1 < a < 1 1 𝑎 1 {\displaystyle{\displaystyle-1<a<1}} / rank
 
Normal rank

Revision as of 16:04, 30 December 2019

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DLMF:4.40.E9
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    Statements

    - e a x ( cosh ( 1 2 x ) ) 2 d x = 4 π a sin ( π a ) , superscript subscript superscript 𝑒 𝑎 𝑥 superscript 1 2 𝑥 2 𝑥 4 𝜋 𝑎 𝜋 𝑎 {\displaystyle{\displaystyle\int_{-\infty}^{\infty}\frac{e^{ax}}{\left(\cosh% \left(\tfrac{1}{2}x\right)\right)^{2}}\mathrm{d}x=\frac{4\pi a}{\sin\left(\pi a% \right)},}}
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    - 1 < a < 1 1 𝑎 1 {\displaystyle{\displaystyle-1<a<1}}
    0 references