DLMF:16.15.E2 (Q5264): 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
			${\displaystyle{\displaystyle\Re\gamma^{\prime}>\Re\beta^{\prime}>0}}$ \realpart@@{\gamma^{\prime}}>\realpart@@{\beta^{\prime}}>0
		Property / constraint: ${\displaystyle{\displaystyle\Re\gamma^{\prime}>\Re\beta^{\prime}>0}}$ / rank
			Normal rank
		Property / Symbols used
			second Appell function
		Property / Symbols used: second Appell function / rank
			Normal rank
		Property / Symbols used: second Appell function / qualifier
			Defining formula: ${\displaystyle{\displaystyle{F_{2}}\left(\NVar{\alpha};\NVar{\beta},\NVar{\beta^{\prime}};\NVar{\gamma},missing;missing,missing\right)\)\@add@PDF@RDFa@triples\end{document}}}$ \AppellF{2}@{\NVar{\alpha}}{\NVar{\beta}}{\NVar{\beta^{\prime}}}{\NVar{\gamma}% }{\NVar{\gamma^{\prime}}}{\NVar{x}}{\NVar{y}}
		Property / Symbols used: second Appell function / qualifier
			xml-id: C16.S13.E2.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.m2aadec
		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.m1aadec
		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.m3aadec
		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.m1aadec

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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.E2	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle{F_{2}}\left(\alpha;\beta,\beta^{\prime};\gamma,\gamma^{\prime};x,y\right)=\frac{\Gamma\left(\gamma\right)\Gamma\left(\gamma^{\prime}\right)}{\Gamma\left(\beta\right)\Gamma\left(\beta^{\prime}\right)\Gamma\left(\gamma-\beta\right)\Gamma\left(\gamma^{\prime}-\beta^{\prime}\right)}\int_{0}^{1}\!\!\!\int_{0}^{1}\frac{u^{\beta-1}v^{\beta^{\prime}-1}(1-u)^{\gamma-\beta-1}(1-v)^{\gamma^{\prime}-\beta^{\prime}-1}}{(1-ux-vy)^{\alpha}}\mathrm{d}u\mathrm{d}v,}}$

0 references

DLMF id

DLMF:16.15.E2

0 references

constraint

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

0 references

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

0 references

Symbols used

second Appell function

Defining formula

${\displaystyle{\displaystyle{F_{2}}\left(\NVar{\alpha};\NVar{\beta},\NVar{\beta^{\prime}};\NVar{\gamma},missing;missing,missing\right)\)\@add@PDF@RDFa@triples\end{document}}}$

xml-id

C16.S13.E2.m2adec

0 references

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2aadec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1aadec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3aadec

0 references

Q10811

Defining formula

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

xml-id

C1.S9.E2.m1aadec

0 references

 

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