DLMF:7.18.E9 (Q2459): Difference between revisions

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Revision as of 13:23, 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 13:32, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols used
			gamma function
		Property / Symbols used: gamma function / rank
			Normal rank
		Property / Symbols used: gamma function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$ \EulerGamma@{\NVar{z}}
		Property / Symbols used: gamma function / qualifier
			xml-id: C5.S2.E1.m2abdec
		Property / Symbols used
			$$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
		Property / Symbols used: $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function / rank
			Normal rank
		Property / Symbols used: $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function / qualifier
			Defining formula: ${\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}$ \KummerconfhyperM@{\NVar{a}}{\NVar{b}}{\NVar{z}}
		Property / Symbols used: $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function / qualifier
			xml-id: C13.S2.E2.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.m2acdec
		Property / Symbols used
			repeated integrals of the complementary error function
		Property / Symbols used: repeated integrals of the complementary error function / rank
			Normal rank
		Property / Symbols used: repeated integrals of the complementary error function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathop{\mathrm{i}^{\NVar{n}}\mathrm{erfc}}\left(\NVar{z}\right)}}$ \repinterfc{\NVar{n}}@{\NVar{z}}
		Property / Symbols used: repeated integrals of the complementary error function / qualifier
			xml-id: C7.S18.E2.m2aidec
		Property / Symbols used
			Q11312
		Property / Symbols used: Q11312 / rank
			Normal rank
		Property / Symbols used: Q11312 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11312 / qualifier
			xml-id: C7.S1.XMD2.m1hdec
		Property / Symbols used
			Q11314
		Property / Symbols used: Q11314 / rank
			Normal rank
		Property / Symbols used: Q11314 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11314 / qualifier
			xml-id: C7.S1.XMD3.m1hdec

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Latest revision as of 13:32, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:7.18.E9	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(z\right)=e^{-z^{2}}\left(\frac{1}{2^{n}\Gamma\left(\tfrac{1}{2}n+1\right)}M\left(\tfrac{1}{2}n+\tfrac{1}{2},\tfrac{1}{2},z^{2}\right)-\frac{z}{2^{n-1}\Gamma\left(\tfrac{1}{2}n+\tfrac{1}{2}\right)}M\left(\tfrac{1}{2}n+1,\tfrac{3}{2},z^{2}\right)\right),}}$

0 references

DLMF id

DLMF:7.18.E9

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2abdec

0 references

$$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function

Defining formula

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

xml-id

C13.S2.E2.m2adec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2acdec

0 references

repeated integrals of the complementary error function

Defining formula

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

xml-id

C7.S18.E2.m2aidec

0 references

Q11312

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C7.S1.XMD2.m1hdec

0 references

Q11314

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C7.S1.XMD3.m1hdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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