Difference between revisions of "DLMF:5.6.E5 (Q2072)"

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Revision as of 15:04, 30 December 2019 Admin (talk | contribs) (‎Changed an Item: Add constraint) ← Older edit		Latest revision as of 17:32, 1 January 2020 Admin (talk | contribs) (‎Changed an Item: Add constraint)
(4 intermediate revisions by the same user not shown)
		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.m2addec
		Property / Symbols used
		+	psi (or digamma) function
		Property / Symbols used: psi (or digamma) function / rank
		+	Normal rank
		Property / Symbols used: psi (or digamma) function / qualifier
		+	Defining formula: ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$ \digamma@{\NVar{z}}
		Property / Symbols used: psi (or digamma) function / qualifier
		+	xml-id: C5.S2.E2.m2adec
		Property / Symbols used
		+	exponential function
		Property / Symbols used: exponential function / rank
		+	Normal rank
		Property / Symbols used: exponential function / qualifier
		+	Defining formula: ${\displaystyle{\displaystyle\exp\NVar{z}}}$ \exp@@{\NVar{z}}
		Property / Symbols used: exponential function / qualifier
		+	xml-id: C4.S2.E19.m2adec
		Property / Symbols used
		+	Q11282
		Property / Symbols used: Q11282 / rank
		+	Normal rank
		Property / Symbols used: Q11282 / qualifier
		+	Defining formula: ${\displaystyle{\displaystyle s}}$ s
		Property / Symbols used: Q11282 / qualifier
		+	xml-id: C5.S1.XMD11.m1adec
		Property / Symbols used
		+	Q11281
		Property / Symbols used: Q11281 / rank
		+	Normal rank
		Property / Symbols used: Q11281 / qualifier
		+	Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11281 / qualifier
		+	xml-id: C5.S1.XMD5.m1ddec

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Latest revision as of 17:32, 1 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:5.6.E5	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\exp\left((1-s)\psi\left(x+s^{1/2}\right)\right)\leq\frac{\Gamma\left(x+1\right)}{\Gamma\left(x+s\right)}\leq\exp\left((1-s)\psi\left(x+\tfrac{1}{2}(s+1)\right)\right),}}$

0 references

DLMF id

DLMF:5.6.E5

0 references

constraint

${\displaystyle{\displaystyle 0<s<1}}$

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2addec

0 references

psi (or digamma) function

Defining formula

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

xml-id

C5.S2.E2.m2adec

0 references

exponential function

Defining formula

${\displaystyle{\displaystyle\exp\NVar{z}}}$

xml-id

C4.S2.E19.m2adec

0 references

Q11282

Defining formula

${\displaystyle{\displaystyle s}}$

xml-id

C5.S1.XMD11.m1adec

0 references

Q11281

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C5.S1.XMD5.m1ddec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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