DLMF:17.13.E3 (Q5468): Difference between revisions

From DRMF

Jump to navigation Jump to search

Revision as of 16:01, 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 15:11, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
(5 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.m2adec
		Property / Symbols used
			Q10770
		Property / Symbols used: Q10770 / rank
			Normal rank
		Property / Symbols used: Q10770 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$ \diff{\NVar{x}}
		Property / Symbols used: Q10770 / qualifier
			xml-id: C1.S4.SS4.m1adec
		Property / Symbols used
			Q10771
		Property / Symbols used: Q10771 / rank
			Normal rank
		Property / Symbols used: Q10771 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\int}}$ \int
		Property / Symbols used: Q10771 / qualifier
			xml-id: C1.S4.SS4.m3abdec
		Property / Symbols used
			$$q$$ -gamma function
		Property / Symbols used: $$q$$ -gamma function / rank
			Normal rank
		Property / Symbols used: $$q$$ -gamma function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Gamma_{\NVar{q}}\left(\NVar{z}\right)}}$ \qGamma{\NVar{q}}@{\NVar{z}}
		Property / Symbols used: $$q$$ -gamma function / qualifier
			xml-id: C5.S18.E4.m2aadec
		Property / Symbols used
			Q11298
		Property / Symbols used: Q11298 / rank
			Normal rank
		Property / Symbols used: Q11298 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$ \qPochhammer{\NVar{a}}{\NVar{q}}{\NVar{n}}
		Property / Symbols used: Q11298 / qualifier
			xml-id: C17.S2.SS1.p1.m2abdec
		Property / Symbols used
			Q11710
		Property / Symbols used: Q11710 / rank
			Normal rank
		Property / Symbols used: Q11710 / qualifier
			Defining formula: ${\displaystyle{\displaystyle q}}$ q
		Property / Symbols used: Q11710 / qualifier
			xml-id: C17.S1.XMD10.m1bdec

---

Latest revision as of 15:11, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:17.13.E3	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{0}^{\infty}t^{\alpha-1}\frac{\left(-tq^{\alpha+\beta};q\right)_{\infty}}{\left(-t;q\right)_{\infty}}\mathrm{d}t=\frac{\Gamma\left(\alpha\right)\Gamma\left(1-\alpha\right)\Gamma_{q}\left(\beta\right)}{\Gamma_{q}\left(1-\alpha\right)\Gamma_{q}\left(\alpha+\beta\right)},}}$

0 references

DLMF id

DLMF:17.13.E3

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2adec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1adec

0 references

Q10771

Defining formula

${\displaystyle{\displaystyle\int}}$

xml-id

C1.S4.SS4.m3abdec

0 references

$$q$$ -gamma function

Defining formula

${\displaystyle{\displaystyle\Gamma_{\NVar{q}}\left(\NVar{z}\right)}}$

xml-id

C5.S18.E4.m2aadec

0 references

Q11298

Defining formula

${\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}$

xml-id

C17.S2.SS1.p1.m2abdec

0 references

Q11710

Defining formula

${\displaystyle{\displaystyle q}}$

xml-id

C17.S1.XMD10.m1bdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5468&oldid=55143"