DLMF:12.5.E4 (Q4118): Difference between revisions

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Property / constraint
 

ℜ ⁡ a < 1 2 𝑎 1 2 {\displaystyle{\displaystyle\Re a<\tfrac{1}{2}}}

\realpart@@{a}<\tfrac{1}{2}
Property / constraint: ℜ ⁡ a < 1 2 𝑎 1 2 {\displaystyle{\displaystyle\Re a<\tfrac{1}{2}}} / rank
 
Normal rank

Revision as of 16:43, 30 December 2019

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DLMF:12.5.E4
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    Statements

    test
    U ⁡ ( a , z ) = 2 π ⁢ e 1 4 ⁢ z 2 ⁢ ∫ 0 ∞ t - a - 1 2 ⁢ e - 1 2 ⁢ t 2 ⁢ cos ⁡ ( z ⁢ t + ( 1 2 ⁢ a + 1 4 ) ⁢ π ) ⁢ d t , parabolic-U 𝑎 𝑧 2 𝜋 superscript 𝑒 1 4 superscript 𝑧 2 superscript subscript 0 superscript 𝑡 𝑎 1 2 superscript 𝑒 1 2 superscript 𝑡 2 𝑧 𝑡 1 2 𝑎 1 4 𝜋 𝑡 {\displaystyle{\displaystyle U\left(a,z\right)=\sqrt{\frac{2}{\pi}}e^{\frac{1}% {4}z^{2}}\*\int_{0}^{\infty}t^{-a-\frac{1}{2}}e^{-\frac{1}{2}t^{2}}\cos\left(% zt+\left(\tfrac{1}{2}a+\tfrac{1}{4}\right)\pi\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:12.5.E4
    0 references
    constraint
    ℜ ⁡ a < 1 2 𝑎 1 2 {\displaystyle{\displaystyle\Re a<\tfrac{1}{2}}}
    0 references
     
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