DLMF:16.11.E11 (Q5245): Difference between revisions

From DRMF

Jump to navigation Jump to search

← Older edit

Revision as of 14:39, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:40, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
(6 intermediate revisions by the same user not shown)
		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.m1fdec
		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.m1hdec
		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.m1gdec
		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.m1hdec
		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.m1hdec
		Property / Symbols used
			Q11708
		Property / Symbols used: Q11708 / rank
			Normal rank
		Property / Symbols used: Q11708 / qualifier
			Defining formula: ${\displaystyle{\displaystyle r}}$ r
		Property / Symbols used: Q11708 / qualifier
			xml-id: C16.S11.XMD6.m1adec

---

Latest revision as of 14:40, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:16.11.E11	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle{{}_{p}F_{q}}\left({a_{1}+r,\dots,a_{p}+r\atop b_{1}+r,\dots,b_{q}+r};z\right)=\sum_{n=0}^{m-1}\frac{{\left(a_{1}+r\right)_{n}}\cdots{\left(a_{p}+r\right)_{n}}}{{\left(b_{1}+r\right)_{n}}\cdots{\left(b_{q}+r\right)_{n}}}\frac{z^{n}}{n!}+O\left(\frac{1}{r^{(q-p)m}}\right),}}$

0 references

DLMF id

DLMF:16.11.E11

0 references

Symbols used

order not exceeding

Defining formula

${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$

xml-id

C2.S1.E3.m2aadec

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.m1aedec

0 references

Q10759

Defining formula

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

xml-id

C5.S2.SS3.m1abdec

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.m1fdec

0 references

Q11691

Defining formula

${\displaystyle{\displaystyle q}}$

xml-id

C16.S1.XMD2.m1hdec

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.m1hdec

0 references

Q11694

Defining formula

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

xml-id

C16.S1.XMD5.m1hdec

0 references

Q11708

Defining formula

${\displaystyle{\displaystyle r}}$

xml-id

C16.S11.XMD6.m1adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5245&oldid=49570"