做假哥伦比亚学院芝加哥校区文凭毕业证【仿证微CXFK69】bighh

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1: 7.18 Repeated Integrals of the Complementary Error Function

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7.18.12 $${\mathrm{i}}^n\mathrm{erfc}\left(z\right)=\frac{1}{\sqrt{2^{n-1}\pi }}{\mathrm{𝐻ℎ}}_n\left(\sqrt{2}z\right).$$

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Defines:

${\mathrm{𝐻ℎ}}_n\left(z\right)$: probability function

Symbols:

$\pi$: the ratio of the circumference of a circle to its diameter, ${\mathrm{i}}^n\mathrm{erfc}\left(z\right)$: repeated integrals of the complementary error function, $z$: complex variable and $n$: nonnegative integer

A&S Ref:

7.2.10

Referenced by:

§12.7(ii)

Permalink:

http://dlmf.nist.gov/7.18.E12

Encodings:

pMML, png, TeX

See also:

Annotations for §7.18(iv), §7.18(iv), §7.18 and Ch.7

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2: 12.7 Relations to Other Functions

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12.7.7 $$U(n+\frac{1}{2},z)={\mathrm{e}}^{\frac{1}{4}{z}^2}{\mathrm{𝐻ℎ}}_n\left(z\right)=\sqrt{\pi }{\mathrm{\hspace{0.17em}2}}^{\frac{1}{2}(n-1)}{\mathrm{e}}^{\frac{1}{4}{z}^2}{\mathrm{i}}^n\mathrm{erfc}\left(z/\sqrt{2}\right),$$ $n=-1,0,1,\mathrm{\dots }$.

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Symbols:

${\mathrm{𝐻ℎ}}_n\left(z\right)$: probability function, $\pi$: the ratio of the circumference of a circle to its diameter, $\mathrm{e}$: base of natural logarithm, $U(a,z)$: parabolic cylinder function, ${\mathrm{i}}^n\mathrm{erfc}\left(z\right)$: repeated integrals of the complementary error function, $z$: complex variable and $n$: nonnegative integer

Referenced by:

§12.7(ii)

Permalink:

http://dlmf.nist.gov/12.7.E7

Encodings:

pMML, png, TeX

See also:

Annotations for §12.7(ii), §12.7 and Ch.12

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