DLMF:12.12.E4 (Q4229): 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 16:44, 30 December 2019

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DLMF:12.12.E4
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    Statements

    test
    ( U ⁡ ( a , z ) ) 2 + ( U ¯ ⁡ ( a , z ) ) 2 = 2 3 2 π ⁢ Γ ⁡ ( 1 2 - a ) ⁢ ∫ 0 ∞ e 2 ⁢ a ⁢ t + 1 2 ⁢ z 2 ⁢ tanh ⁡ t sinh ⁡ ( 2 ⁢ t ) ⁢ d t , superscript parabolic-U 𝑎 𝑧 2 superscript parabolic-U-bar 𝑎 𝑧 2 superscript 2 3 2 𝜋 Euler-Gamma 1 2 𝑎 superscript subscript 0 superscript 𝑒 2 𝑎 𝑡 1 2 superscript 𝑧 2 𝑡 2 𝑡 𝑡 {\displaystyle{\displaystyle(U\left(a,z\right))^{2}+(\overline{U}\left(a,z% \right))^{2}=\frac{2^{\frac{3}{2}}}{\pi}\Gamma\left(\tfrac{1}{2}-a\right)\int_% {0}^{\infty}\frac{e^{2at+\frac{1}{2}z^{2}\tanh t}}{\sqrt{\sinh\left(2t\right)}% }\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:12.12.E4
    0 references
    constraint
    ℜ ⁡ a < 1 2 𝑎 1 2 {\displaystyle{\displaystyle\Re a<\tfrac{1}{2}}}
    0 references
     
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