DLMF:12.5.E7 (Q4121): Difference between revisions

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Property / constraint
 

c > 0 𝑐 0 {\displaystyle{\displaystyle c>0}}

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

Revision as of 16:43, 30 December 2019

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DLMF:12.5.E7
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    Statements

    test
    V ⁡ ( a , z ) = e - 1 4 ⁢ z 2 2 ⁢ π ⁢ ( ∫ - i ⁢ c - ∞ - i ⁢ c + ∞ + ∫ i ⁢ c - ∞ i ⁢ c + ∞ ) ⁢ e z ⁢ t - 1 2 ⁢ t 2 ⁢ t a - 1 2 ⁢ d t , parabolic-V 𝑎 𝑧 superscript 𝑒 1 4 superscript 𝑧 2 2 𝜋 superscript subscript 𝑖 𝑐 𝑖 𝑐 superscript subscript 𝑖 𝑐 𝑖 𝑐 superscript 𝑒 𝑧 𝑡 1 2 superscript 𝑡 2 superscript 𝑡 𝑎 1 2 𝑡 {\displaystyle{\displaystyle V\left(a,z\right)=\frac{e^{-\frac{1}{4}z^{2}}}{2% \pi}\*\left(\int_{-ic-\infty}^{-ic+\infty}+\int_{ic-\infty}^{ic+\infty}\right)% e^{zt-\frac{1}{2}t^{2}}t^{a-\frac{1}{2}}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:12.5.E7
    0 references
    constraint
    - π < ph ⁡ t < π 𝜋 phase 𝑡 𝜋 {\displaystyle{\displaystyle-\pi<\operatorname{ph}{t}<\pi}}
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    - π < ph ⁡ t < π 𝜋 ph 𝑡 𝜋 {\displaystyle{\displaystyle-\pi<\operatorname{ph}{t}<\pi}}
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    c > 0 𝑐 0 {\displaystyle{\displaystyle c>0}}
    0 references
     
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