DLMF:12.7.E6 (Q4129): Difference between revisions

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Revision as of 15:16, 29 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Created a new Item: Wikidata Toolkit example test item creation		Latest revision as of 15:12, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / constraint
			${\displaystyle{\displaystyle n=0,1,2,\dots}}$ n=0,1,2,\dots
		Property / constraint: ${\displaystyle{\displaystyle n=0,1,2,\dots}}$ / rank
			Normal rank
		Property / Symbols used
			Q11515
		Property / Symbols used: Q11515 / rank
			Normal rank
		Property / Symbols used: Q11515 / qualifier
			Defining formula: ${\displaystyle{\displaystyle D_{\NVar{\nu}}\left(\NVar{z}\right)}}$ \WhittakerparaD{\NVar{\nu}}@{\NVar{z}}
		Property / Symbols used: Q11515 / qualifier
			xml-id: C12.S1.p3.m6acdec
		Property / Symbols used
			the ratio of the circumference of a circle to its diameter
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
			Normal rank
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			Defining formula: ${\displaystyle{\displaystyle\pi}}$ \cpi
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			xml-id: C3.S12.E1.m2acdec
		Property / Symbols used
			complementary error function
		Property / Symbols used: complementary error function / rank
			Normal rank
		Property / Symbols used: complementary error function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}$ \erfc@@{\NVar{z}}
		Property / Symbols used: complementary error function / qualifier
			xml-id: C7.S2.E2.m2aadec
		Property / Symbols used
			derivative of $$f$$ with respect to $$x$$
		Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / rank
			Normal rank
		Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
			Defining formula: ${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$ \deriv{\NVar{f}}{\NVar{x}}
		Property / Symbols used: derivative of $$f$$ with respect to $$x$$ / qualifier
			xml-id: C1.S4.E4.m2adec
		Property / Symbols used
			base of natural logarithm
		Property / Symbols used: base of natural logarithm / rank
			Normal rank
		Property / Symbols used: base of natural logarithm / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{e}}}$ \expe
		Property / Symbols used: base of natural logarithm / qualifier
			xml-id: C4.S2.E11.m2aedec
		Property / Symbols used
			Q10755
		Property / Symbols used: Q10755 / rank
			Normal rank
		Property / Symbols used: Q10755 / qualifier
			Defining formula: ${\displaystyle{\displaystyle!}}$ !
		Property / Symbols used: Q10755 / qualifier
			xml-id: introduction.Sx4.p1.t1.r15.m5adec
		Property / Symbols used
			Q11320
		Property / Symbols used: Q11320 / rank
			Normal rank
		Property / Symbols used: Q11320 / qualifier
			Defining formula: ${\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}$ \paraU@{\NVar{a}}{\NVar{z}}
		Property / Symbols used: Q11320 / qualifier
			xml-id: C12.S2.SS1.p1.m1acdec
		Property / Symbols used
			Q11513
		Property / Symbols used: Q11513 / rank
			Normal rank
		Property / Symbols used: Q11513 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11513 / qualifier
			xml-id: C12.S1.XMD3.m1edec
		Property / Symbols used
			Q11518
		Property / Symbols used: Q11518 / rank
			Normal rank
		Property / Symbols used: Q11518 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11518 / qualifier
			xml-id: C12.S1.XMD4.m1bdec

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Latest revision as of 15:12, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:12.7.E6	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle U\left(n+\tfrac{1}{2},z\right)=D_{-n-1}\left(z\right)=\sqrt{\frac{\pi}{2}}\frac{(-1)^{n}}{n!}e^{-\frac{1}{4}z^{2}}\frac{{\mathrm{d}}^{n}\left(e^{\frac{1}{2}z^{2}}\operatorname{erfc}\left(z/\sqrt{2}\right)\right)}{{\mathrm{d}z}^{n}},}}$

0 references

DLMF id

DLMF:12.7.E6

0 references

constraint

${\displaystyle{\displaystyle n=0,1,2,\dots}}$

0 references

Symbols used

Q11515

Defining formula

${\displaystyle{\displaystyle D_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C12.S1.p3.m6acdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

${\displaystyle{\displaystyle\pi}}$

xml-id

C3.S12.E1.m2acdec

0 references

complementary error function

Defining formula

${\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}$

xml-id

C7.S2.E2.m2aadec

0 references

derivative of $$f$$ with respect to $$x$$

Defining formula

${\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}$

xml-id

C1.S4.E4.m2adec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2aedec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5adec

0 references

Q11320

Defining formula

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

xml-id

C12.S2.SS1.p1.m1acdec

0 references

Q11513

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C12.S1.XMD3.m1edec

0 references

Q11518

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C12.S1.XMD4.m1bdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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