DLMF:16.15.E3 (Q5265): Difference between revisions

Revision as of 14:41, 2 January 2020

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Language	Label	Description	Also known as
English	DLMF:16.15.E3	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle{F_{3}}\left(\alpha,\alpha^{\prime};\beta,\beta^{% \prime};\gamma;x,y\right)=\frac{\Gamma\left(\gamma\right)}{\Gamma\left(\beta% \right)\Gamma\left(\beta^{\prime}\right)\Gamma\left(\gamma-\beta-\beta^{\prime% }\right)}\iint_{\Delta}\frac{u^{\beta-1}v^{\beta^{\prime}-1}(1-u-v)^{\gamma-% \beta-\beta^{\prime}-1}}{(1-ux)^{\alpha}(1-vy)^{\alpha^{\prime}}}\mathrm{d}u% \mathrm{d}v,}}

0 references

DLMF id

DLMF:16.15.E3

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constraint

{\displaystyle{\displaystyle\Re(\gamma-\beta-\beta^{\prime})>0}}

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

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

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Symbols used

third Appell function

Defining formula

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "XMLReader::XML(): Argument #1 ($source) cannot be empty"): {\displaystyle \AppellF{3}@{\NVar{\alpha}}{\NVar{\alpha^{\prime}}}{\NVar{\beta}}{\NVar{\beta^% {\prime}}}{\NVar{\gamma}}{\NVar{x}}{\NVar{y}}}

xml-id

C16.S13.E3.m2adec

0 references

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2abdec

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Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1abdec

0 references

@@ 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.m1abdec

DLMF:16.15.E3 (Q5265): Difference between revisions

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

Revision as of 14:41, 2 January 2020

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DLMF:16.15.E3 (Q5265): Difference between revisions

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

Revision as of 14:41, 2 January 2020

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