DLMF:12.13.E6 (Q4235): Difference between revisions

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Revision as of 17:44, 30 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:26, 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
			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.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.m5abdec
		Property / Symbols used
			Q11169
		Property / Symbols used: Q11169 / rank
			Normal rank
		Property / Symbols used: Q11169 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}$ \floor{\NVar{x}}
		Property / Symbols used: Q11169 / qualifier
			xml-id: introduction.Sx4.p1.t1.r17.m4adec
		Property / Symbols used
			imaginary unit
		Property / Symbols used: imaginary unit / rank
			Normal rank
		Property / Symbols used: imaginary unit / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{i}}}$ \iunit
		Property / Symbols used: imaginary unit / qualifier
			xml-id: C1.S9.E1.m2adec
		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.m1dec
		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.m1dec

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Latest revision as of 15:26, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:12.13.E6	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle n!U\left(n+\tfrac{1}{2},z\right)=i^{n}e^{-\frac{1}{2}z^{2}}\operatorname{erfc}(z/\sqrt{2})U\left(-n-\tfrac{1}{2},iz\right)+\sum_{m=1}^{\left\lfloor\frac{1}{2}n+\frac{1}{2}\right\rfloor}U\left(2m-n-\tfrac{1}{2},z\right),}}$

0 references

DLMF id

DLMF:12.13.E6

0 references

constraint

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

0 references

Symbols used

complementary error function

Defining formula

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

xml-id

C7.S2.E2.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.m5abdec

0 references

Q11169

Defining formula

${\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}$

xml-id

introduction.Sx4.p1.t1.r17.m4adec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2adec

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.m1dec

0 references

Q11518

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C12.S1.XMD4.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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