DLMF:10.32.E7 (Q3527): Difference between revisions

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Property / constraint
 

x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}

x>0
Property / constraint: x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}} / rank
 
Normal rank

Revision as of 16:38, 30 December 2019

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DLMF:10.32.E7
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    Statements

    test
    K ν ⁡ ( x ) = sec ⁡ ( 1 2 ⁢ ν ⁢ π ) ⁢ ∫ 0 ∞ cos ⁡ ( x ⁢ sinh ⁡ t ) ⁢ cosh ⁡ ( ν ⁢ t ) ⁢ d t = csc ⁡ ( 1 2 ⁢ ν ⁢ π ) ⁢ ∫ 0 ∞ sin ⁡ ( x ⁢ sinh ⁡ t ) ⁢ sinh ⁡ ( ν ⁢ t ) ⁢ d t , modified-Bessel-second-kind 𝜈 𝑥 1 2 𝜈 𝜋 superscript subscript 0 𝑥 𝑡 𝜈 𝑡 𝑡 1 2 𝜈 𝜋 superscript subscript 0 𝑥 𝑡 𝜈 𝑡 𝑡 {\displaystyle{\displaystyle K_{\nu}\left(x\right)=\sec\left(\tfrac{1}{2}\nu% \pi\right)\int_{0}^{\infty}\cos\left(x\sinh t\right)\cosh\left(\nu t\right)% \mathrm{d}t=\csc\left(\tfrac{1}{2}\nu\pi\right)\int_{0}^{\infty}\sin\left(x% \sinh t\right)\sinh\left(\nu t\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:10.32.E7
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    constraint
    | ℜ ⁡ ν | < 1 𝜈 1 {\displaystyle{\displaystyle|\Re\nu|<1}}
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    | ℜ ⁡ ν | < 1 𝜈 1 {\displaystyle{\displaystyle|\Re\nu|<1}}
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    x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}
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