DLMF:8.11.E12 (Q2585): Difference between revisions

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Revision as of 17:11, 30 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:55, 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
			Q10931
		Property / Symbols used: Q10931 / rank
			Normal rank
		Property / Symbols used: Q10931 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sim}}$ \asympexp
		Property / Symbols used: Q10931 / qualifier
			xml-id: C2.S1.SS3.p1.m11abdec
		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.m2afdec
		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.m2agdec
		Property / Symbols used
			incomplete gamma function
		Property / Symbols used: incomplete gamma function / rank
			Normal rank
		Property / Symbols used: incomplete gamma function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Gamma\left(\NVar{a},\NVar{z}\right)}}$ \incGamma@{\NVar{a}}{\NVar{z}}
		Property / Symbols used: incomplete gamma function / qualifier
			xml-id: C8.S2.E2.m2abdec
		Property / Symbols used
			Q10817
		Property / Symbols used: Q10817 / rank
			Normal rank
		Property / Symbols used: Q10817 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{ph}}}$ \phase
		Property / Symbols used: Q10817 / qualifier
			xml-id: C1.S9.E7.m1addec
		Property / Symbols used
			Q11323
		Property / Symbols used: Q11323 / rank
			Normal rank
		Property / Symbols used: Q11323 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11323 / qualifier
			xml-id: C8.S1.XMD2.m1fdec
		Property / Symbols used
			Q11343
		Property / Symbols used: Q11343 / rank
			Normal rank
		Property / Symbols used: Q11343 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\delta}}$ \delta
		Property / Symbols used: Q11343 / qualifier
			xml-id: C8.S1.XMD7.m1ddec

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Latest revision as of 13:55, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:8.11.E12	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\Gamma\left(z,z\right)\sim z^{z-1}e^{-z}\left(\sqrt{\frac{\pi}{2}}z^{\frac{1}{2}}-\frac{1}{3}+\frac{\sqrt{2\pi}}{24z^{\frac{1}{2}}}-\frac{4}{135z}+\frac{\sqrt{2\pi}}{576z^{\frac{3}{2}}}+\frac{8}{2835z^{2}}+\dots\right),}}$

0 references

DLMF id

DLMF:8.11.E12

0 references

constraint

${\displaystyle{\displaystyle|\operatorname{ph}z|\leq 2\pi-\delta}}$

0 references

Symbols used

Q10931

Defining formula

${\displaystyle{\displaystyle\sim}}$

xml-id

C2.S1.SS3.p1.m11abdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2afdec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2agdec

0 references

incomplete gamma function

Defining formula

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

xml-id

C8.S2.E2.m2abdec

0 references

Q10817

Defining formula

${\displaystyle{\displaystyle\operatorname{ph}}}$

xml-id

C1.S9.E7.m1addec

0 references

Q11323

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C8.S1.XMD2.m1fdec

0 references

Q11343

Defining formula

${\displaystyle{\displaystyle\delta}}$

xml-id

C8.S1.XMD7.m1ddec

0 references

 

Sitelinks

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DRMF related sites(0 entries)

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