DLMF:17.13.E2 (Q5467): Difference between revisions

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Revision as of 15:10, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:11, 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
			$$q$$ -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.m2adec
		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.m2aadec
		Property / Symbols used
			Q11299
		Property / Symbols used: Q11299 / rank
			Normal rank
		Property / Symbols used: Q11299 / qualifier
			Defining formula: ${\displaystyle{\displaystyle{\mathrm{d}}_{\NVar{q}}\NVar{x}}}$ \qdiff{\NVar{q}}{\NVar{x}}
		Property / Symbols used: Q11299 / qualifier
			xml-id: C17.S2.SS5.p1.m3aadec
		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.m1adec
		Property / Symbols used
			Q11719
		Property / Symbols used: Q11719 / rank
			Normal rank
		Property / Symbols used: Q11719 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11719 / qualifier
			xml-id: C17.S1.XMD8.m1adec

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Latest revision as of 15:11, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:17.13.E2	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{-c}^{d}\frac{\left(-qx/c;q\right)_{\infty}\left(qx/d;q\right)_{\infty}}{\left(-xq^{\alpha}/c;q\right)_{\infty}\left(xq^{\beta}/d;q\right)_{\infty}}{\mathrm{d}}_{q}x=\frac{\Gamma_{q}\left(\alpha\right)\Gamma_{q}\left(\beta\right)}{\Gamma_{q}\left(\alpha+\beta\right)}\frac{cd}{c+d}\frac{\left(-c/d;q\right)_{\infty}\left(-d/c;q\right)_{\infty}}{\left(-q^{\beta}c/d;q\right)_{\infty}\left(-q^{\alpha}d/c;q\right)_{\infty}}.}}$

0 references

DLMF id

DLMF:17.13.E2

0 references

Symbols used

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3aadec

0 references

$$q$$ -gamma function

Defining formula

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

xml-id

C5.S18.E4.m2adec

0 references

Q11298

Defining formula

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

xml-id

C17.S2.SS1.p1.m2aadec

0 references

Q11299

Defining formula

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

xml-id

C17.S2.SS5.p1.m3aadec

0 references

Q11710

Defining formula

${\displaystyle{\displaystyle q}}$

xml-id

C17.S1.XMD10.m1adec

0 references

Q11719

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C17.S1.XMD8.m1adec

0 references

 

Sitelinks

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