DLMF:12.7.E7 (Q4130)

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Language	Label	Description	Also known as
English	DLMF:12.7.E7	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle U\left(n+\tfrac{1}{2},z\right)=e^{\frac{1}{4}z^{2% }}\mathit{Hh}_{n}\left(z\right)=\sqrt{\pi}\,2^{\frac{1}{2}(n-1)}e^{\frac{1}{4}% z^{2}}\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(z/\sqrt{2}\right),}}

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DLMF:12.7.E7

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{\displaystyle{\displaystyle n=-1,0,1,\dots}}

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probability function

Defining formula

{\displaystyle{\displaystyle\mathit{Hh}_{\NVar{n}}\left(\NVar{z}\right)}}

C7.S18.E12.m2adec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2addec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2afdec

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Defining formula

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

C12.S2.SS1.p1.m1addec

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repeated integrals of the complementary error function

Defining formula

{\displaystyle{\displaystyle\mathop{\mathrm{i}^{\NVar{n}}\mathrm{erfc}}\left(% \NVar{z}\right)}}

C7.S18.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle z}}

C12.S1.XMD3.m1fdec

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Defining formula

{\displaystyle{\displaystyle n}}

C12.S1.XMD4.m1cdec

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Sitelinks

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