DLMF:16.8.E8 (Q5227): Difference between revisions

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Revision as of 14:36, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:36, 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
			Q11693
		Property / Symbols used: Q11693 / rank
			Normal rank
		Property / Symbols used: Q11693 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}$ a,a_{1},\ldots,a_{p}
		Property / Symbols used: Q11693 / qualifier
			xml-id: C16.S1.XMD4.m1cdec
		Property / Symbols used
			Q11694
		Property / Symbols used: Q11694 / rank
			Normal rank
		Property / Symbols used: Q11694 / qualifier
			Defining formula: ${\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}$ b,b_{1},\ldots,b_{q}
		Property / Symbols used: Q11694 / qualifier
			xml-id: C16.S1.XMD5.m1cdec
		Property / Symbols used
			Q11702
		Property / Symbols used: Q11702 / rank
			Normal rank
		Property / Symbols used: Q11702 / qualifier
			Defining formula: ${\displaystyle{\displaystyle w}}$ w
		Property / Symbols used: Q11702 / qualifier
			xml-id: C16.S8.XMD4.m1edec

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Latest revision as of 14:36, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:16.8.E8	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle{{}_{q+1}F_{q}}\left({a_{1},\dots,a_{q+1}\atop b_{1},\dots,b_{q}};z\right)=\sum_{j=1}^{q+1}\left({\textstyle\ifrac{\prod\limits_{\begin{subarray}{c}k=1\\ k\neq j\end{subarray}}^{q+1}\frac{\Gamma\left(a_{k}-a_{j}\right)}{\Gamma\left(a_{k}\right)}}{\prod\limits_{k=1}^{q}\frac{\Gamma\left(b_{k}-a_{j}\right)}{\Gamma\left(b_{k}\right)}}}\right)\widetilde{w}_{j}(z),}}$

0 references

DLMF id

DLMF:16.8.E8

0 references

constraint

${\displaystyle{\displaystyle|\operatorname{ph}\left(-z\right)|\leq\pi}}$

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2adec

0 references

Q11125

Defining formula

${\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}$

xml-id

C16.S2.m1abdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

${\displaystyle{\displaystyle\pi}}$

xml-id

C3.S12.E1.m2adec

0 references

Q10817

Defining formula

${\displaystyle{\displaystyle\operatorname{ph}}}$

xml-id

C1.S9.E7.m1adec

0 references

Q11691

Defining formula

${\displaystyle{\displaystyle q}}$

xml-id

C16.S1.XMD2.m1edec

0 references

Q11692

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C16.S1.XMD3.m1gdec

0 references

Q11693

Defining formula

${\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}$

xml-id

C16.S1.XMD4.m1cdec

0 references

Q11694

Defining formula

${\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}$

xml-id

C16.S1.XMD5.m1cdec

0 references

Q11702

Defining formula

${\displaystyle{\displaystyle w}}$

xml-id

C16.S8.XMD4.m1edec

0 references

 

Sitelinks

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