DLMF:10.32.E13 (Q3533): Difference between revisions

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Property / constraint
 

c > max ⁡ ( ℜ ⁡ ν , 0 ) , | ph ⁡ z | < 1 2 ⁢ π formulae-sequence 𝑐 𝜈 0 phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle c>\max(\Re\nu,0),|\operatorname{ph}z|<\frac{1}{2}% \pi}}

c>\max(\realpart@@{\nu},0),|\phase@@{z}|<\frac{1}{2}\pi
Property / constraint: c > max ⁡ ( ℜ ⁡ ν , 0 ) , | ph ⁡ z | < 1 2 ⁢ π formulae-sequence 𝑐 𝜈 0 phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle c>\max(\Re\nu,0),|\operatorname{ph}z|<\frac{1}{2}% \pi}} / rank
 
Normal rank

Revision as of 16:38, 30 December 2019

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DLMF:10.32.E13
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    Statements

    test
    K ν ⁡ ( z ) = ( 1 2 ⁢ z ) ν 4 ⁢ π ⁢ i ⁢ ∫ c - i ⁢ ∞ c + i ⁢ ∞ Γ ⁡ ( t ) ⁢ Γ ⁡ ( t - ν ) ⁢ ( 1 2 ⁢ z ) - 2 ⁢ t ⁢ d t , modified-Bessel-second-kind 𝜈 𝑧 superscript 1 2 𝑧 𝜈 4 𝜋 𝑖 superscript subscript 𝑐 𝑖 𝑐 𝑖 Euler-Gamma 𝑡 Euler-Gamma 𝑡 𝜈 superscript 1 2 𝑧 2 𝑡 𝑡 {\displaystyle{\displaystyle K_{\nu}\left(z\right)=\frac{(\frac{1}{2}z)^{\nu}}% {4\pi i}\int_{c-i\infty}^{c+i\infty}\Gamma\left(t\right)\Gamma\left(t-\nu% \right)(\tfrac{1}{2}z)^{-2t}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:10.32.E13
    0 references
    constraint
    c > max ⁡ ( ℜ ⁡ ν , 0 ) , | ph ⁡ z | < 1 2 ⁢ π formulae-sequence 𝑐 𝜈 0 phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle c>\max(\Re\nu,0),|\operatorname{ph}z|<\frac{1}{2}% \pi}}
    0 references
     
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