DLMF:10.43.E21 (Q3635): Difference between revisions

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Property / constraint
 

| a | < 1 𝑎 1 {\displaystyle{\displaystyle|\Im a|<1}}

|\imagpart@@{a}|<1
Property / constraint: | a | < 1 𝑎 1 {\displaystyle{\displaystyle|\Im a|<1}} / rank
 
Normal rank

Revision as of 17:40, 30 December 2019

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DLMF:10.43.E21
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    Statements

    0 sin ( a t ) K 0 ( t ) d t = arcsinh a ( 1 + a 2 ) 1 2 , superscript subscript 0 𝑎 𝑡 modified-Bessel-second-kind 0 𝑡 𝑡 hyperbolic-inverse-sine 𝑎 superscript 1 superscript 𝑎 2 1 2 {\displaystyle{\displaystyle\int_{0}^{\infty}\sin\left(at\right)K_{0}\left(t% \right)\mathrm{d}t=\frac{\operatorname{arcsinh}a}{(1+a^{2})^{\frac{1}{2}}},}}
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    | a | < 1 𝑎 1 {\displaystyle{\displaystyle|\Im a|<1}}
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