DLMF:16.15.E4 (Q5266): Difference between revisions

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Revision as of 17:58, 30 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:41, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / constraint
			${\displaystyle{\displaystyle\Re\gamma^{\prime}>\Re\beta>0}}$ \realpart@@{\gamma^{\prime}}>\realpart@@{\beta}>0
		Property / constraint: ${\displaystyle{\displaystyle\Re\gamma^{\prime}>\Re\beta>0}}$ / rank
			Normal rank
		Property / Symbols used
			fourth Appell function
		Property / Symbols used: fourth Appell function / rank
			Normal rank
		Property / Symbols used: fourth Appell function / qualifier
			Defining formula: ${\displaystyle{\displaystyle{F_{4}}\left(\NVar{\alpha},\NVar{\beta};\NVar{\gamma},\NVar{\gamma^{\prime}}{missing}{missing};missing,missing\right)\)\@add@PDF@RDFa@triples\end{document}}}$ \AppellF{4}@{\NVar{\alpha}}{\NVar{\beta}}{\NVar{\gamma}}{\NVar{\gamma^{\prime}% }}{\NVar{x}}{\NVar{y}}
		Property / Symbols used: fourth Appell function / qualifier
			xml-id: C16.S13.E4.m2adec
		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.m2acdec
		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.m1acdec
		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
			Q10811
		Property / Symbols used: Q10811 / rank
			Normal rank
		Property / Symbols used: Q10811 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Re}}$ \realpart@@
		Property / Symbols used: Q10811 / qualifier
			xml-id: C1.S9.E2.m1acdec

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Latest revision as of 14:41, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:16.15.E4	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle{F_{4}}\left(\alpha,\beta;\gamma,\gamma^{\prime};x(1-y),y(1-x)\right)=\frac{\Gamma\left(\gamma\right)\Gamma\left(\gamma^{\prime}\right)}{\Gamma\left(\alpha\right)\Gamma\left(\beta\right)\Gamma\left(\gamma-\alpha\right)\Gamma\left(\gamma^{\prime}-\beta\right)}\int_{0}^{1}\!\!\!\int_{0}^{1}\frac{u^{\alpha-1}v^{\beta-1}(1-u)^{\gamma-\alpha-1}(1-v)^{\gamma^{\prime}-\beta-1}}{(1-ux)^{\gamma+\gamma^{\prime}-\alpha-1}(1-vy)^{\gamma+\gamma^{\prime}-\beta-1}(1-ux-vy)^{\alpha+\beta-\gamma-\gamma^{\prime}+1}}\mathrm{d}u\mathrm{d}v,}}$

0 references

DLMF id

DLMF:16.15.E4

0 references

constraint

${\displaystyle{\displaystyle\Re\gamma>\Re\alpha>0}}$

0 references

${\displaystyle{\displaystyle\Re\gamma^{\prime}>\Re\beta>0}}$

0 references

Symbols used

fourth Appell function

Defining formula

${\displaystyle{\displaystyle{F_{4}}\left(\NVar{\alpha},\NVar{\beta};\NVar{\gamma},\NVar{\gamma^{\prime}}{missing}{missing};missing,missing\right)\)\@add@PDF@RDFa@triples\end{document}}}$

xml-id

C16.S13.E4.m2adec

0 references

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2acdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1acdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3abdec

0 references

Q10811

Defining formula

${\displaystyle{\displaystyle\Re}}$

xml-id

C1.S9.E2.m1acdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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