DLMF:12.5.E9 (Q4123): Difference between revisions

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Property / constraint
 

| ph z | < 1 4 π phase 𝑧 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{4}\pi}}

|\phase@@{z}|<\tfrac{1}{4}\pi
Property / constraint: | ph z | < 1 4 π phase 𝑧 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{4}\pi}} / rank
 
Normal rank

Revision as of 17:44, 30 December 2019

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DLMF:12.5.E9
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    V ( a , z ) = 2 π e 1 4 z 2 z a - 1 2 2 π i Γ ( 1 2 - a ) - i i Γ ( t ) Γ ( 1 2 - a - 2 t ) 2 t z 2 t cos ( π t ) d t , parabolic-V 𝑎 𝑧 2 𝜋 superscript 𝑒 1 4 superscript 𝑧 2 superscript 𝑧 𝑎 1 2 2 𝜋 𝑖 Euler-Gamma 1 2 𝑎 superscript subscript 𝑖 𝑖 Euler-Gamma 𝑡 Euler-Gamma 1 2 𝑎 2 𝑡 superscript 2 𝑡 superscript 𝑧 2 𝑡 𝜋 𝑡 𝑡 {\displaystyle{\displaystyle V\left(a,z\right)=\sqrt{\frac{2}{\pi}}\frac{e^{% \frac{1}{4}z^{2}}z^{a-\frac{1}{2}}}{2\pi i\Gamma\left(\frac{1}{2}-a\right)}\*% \int_{-i\infty}^{i\infty}\Gamma\left(t\right)\Gamma\left(\tfrac{1}{2}-a-2t% \right)2^{t}z^{2t}\cos\left(\pi t\right)\mathrm{d}t,}}
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    DLMF:12.5.E9
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    | ph z | < 1 4 π phase 𝑧 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{4}\pi}}
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