DLMF:12.5.E8 (Q4122): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:12.5.E8	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle U\left(a,z\right)=\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}% \mathrm{d}t,}}

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DLMF:12.5.E8

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{\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{3}{4}\pi}}

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{\displaystyle{\displaystyle a\neq-\frac{1}{2},-\frac{3}{2},-\frac{5}{2},\dots}}

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{\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{3}{4}\pi}}

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2addec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2afdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1agdec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2agdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2acdec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3agdec

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Defining formula

{\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}

C12.S2.SS1.p1.m1afdec

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Defining formula

{\displaystyle{\displaystyle\operatorname{ph}}}

C1.S9.E7.m1aedec

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Defining formula

{\displaystyle{\displaystyle z}}

C12.S1.XMD3.m1gdec

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Defining formula

{\displaystyle{\displaystyle a}}

C12.S1.XMD6.m1gdec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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