DLMF:16.2.E5 (Q5187): Difference between revisions

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Revision as of 14:28, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:28, 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
			Q10755
		Property / Symbols used: Q10755 / rank
			Normal rank
		Property / Symbols used: Q10755 / qualifier
			Defining formula: ${\displaystyle{\displaystyle!}}$ !
		Property / Symbols used: Q10755 / qualifier
			xml-id: introduction.Sx4.p1.t1.r15.m5abdec
		Property / Symbols used
			Q11690
		Property / Symbols used: Q11690 / rank
			Normal rank
		Property / Symbols used: Q11690 / qualifier
			Defining formula: ${\displaystyle{\displaystyle p}}$ p
		Property / Symbols used: Q11690 / qualifier
			xml-id: C16.S1.XMD1.m1cdec
		Property / Symbols used
			Q11691
		Property / Symbols used: Q11691 / rank
			Normal rank
		Property / Symbols used: Q11691 / qualifier
			Defining formula: ${\displaystyle{\displaystyle q}}$ q
		Property / Symbols used: Q11691 / qualifier
			xml-id: C16.S1.XMD2.m1ddec
		Property / Symbols used
			Q11692
		Property / Symbols used: Q11692 / rank
			Normal rank
		Property / Symbols used: Q11692 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11692 / qualifier
			xml-id: C16.S1.XMD3.m1cdec
		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.m1bdec
		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.m1bdec

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Latest revision as of 14:28, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:16.2.E5	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle{{}_{p}{\mathbf{F}}_{q}}\left(\mathbf{a};\mathbf{b};z\right)=\ifrac{{{}_{p}F_{q}}\left({a_{1},\dots,a_{p}\atop b_{1},\dots,b_{q}};z\right)}{\left(\Gamma\left(b_{1}\right)\cdots\Gamma\left(b_{q}\right)\right)}=\sum_{k=0}^{\infty}\frac{{\left(a_{1}\right)_{k}}\cdots{\left(a_{p}\right)_{k}}}{\Gamma\left(b_{1}+k\right)\cdots\Gamma\left(b_{q}+k\right)}\frac{z^{k}}{k!};}}$

0 references

DLMF id

DLMF:16.2.E5

0 references

Symbols defined

scaled (or Olver’s) generalized hypergeometric function

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.m1acdec

0 references

Q10759

Defining formula

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

xml-id

C5.S2.SS3.m1acdec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5abdec

0 references

Q11690

Defining formula

${\displaystyle{\displaystyle p}}$

xml-id

C16.S1.XMD1.m1cdec

0 references

Q11691

Defining formula

${\displaystyle{\displaystyle q}}$

xml-id

C16.S1.XMD2.m1ddec

0 references

Q11692

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C16.S1.XMD3.m1cdec

0 references

Q11693

Defining formula

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

xml-id

C16.S1.XMD4.m1bdec

0 references

Q11694

Defining formula

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

xml-id

C16.S1.XMD5.m1bdec

0 references

 

Sitelinks

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