DLMF:16.12.E3 (Q5248): Difference between revisions

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Revision as of 15:53, 29 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Created a new Item: Wikidata Toolkit example test item creation		Latest revision as of 14:40, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
(7 intermediate revisions by the same user not shown)
		Property / constraint
			${\displaystyle{\displaystyle|z|<1}}$ |z|<1
		Property / constraint: ${\displaystyle{\displaystyle|z|<1}}$ / rank
			Normal rank
		Property / Symbols used
			Q11581
		Property / Symbols used: Q11581 / rank
			Normal rank
		Property / Symbols used: Q11581 / qualifier
			Defining formula: ${\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$ \genhyperF{2}{1}@{\NVar{a},\NVar{b}}{\NVar{c}}{\NVar{z}}
		Property / Symbols used: Q11581 / qualifier
			xml-id: C16.S2.m5aadec
		Property / Symbols used
			Q11125
		Property / Symbols used: Q11125 / rank
			Normal rank
		Property / Symbols used: Q11125 / qualifier
			Defining formula: ${\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}$ \genhyperF{\NVar{p}}{\NVar{q}}@{\NVar{a_{1},\dots,a_{p}}}{\NVar{b_{1},\dots,b_{q}}}{\NVar{z}}
		Property / Symbols used: Q11125 / qualifier
			xml-id: C16.S2.m1abdec
		Property / Symbols used
			Q10759
		Property / Symbols used: Q10759 / rank
			Normal rank
		Property / Symbols used: Q10759 / qualifier
			Defining formula: ${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$ \Pochhammersym{\NVar{a}}{\NVar{n}}
		Property / Symbols used: Q10759 / qualifier
			xml-id: C5.S2.SS3.m1adec
		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.m5adec
		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.m1bdec
		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 14:40, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:16.12.E3	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\left({{}_{2}F_{1}}\left({a,b\atop c};z\right)\right)^{2}=\sum_{k=0}^{\infty}\frac{{\left(2a\right)_{k}}{\left(2b\right)_{k}}{\left(c-\frac{1}{2}\right)_{k}}}{{\left(c\right)_{k}}{\left(2c-1\right)_{k}}k!}{{}_{4}F_{3}}\left({-\frac{1}{2}k,\frac{1}{2}(1-k),a+b-c+\frac{1}{2},\frac{1}{2}\atop a+\frac{1}{2},b+\frac{1}{2},\frac{3}{2}-k-c};1\right)z^{k},}}$

0 references

DLMF id

DLMF:16.12.E3

0 references

constraint

${\displaystyle{\displaystyle|z|<1}}$

0 references

Symbols used

Q11581

Defining formula

${\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$

xml-id

C16.S2.m5aadec

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

Q10759

Defining formula

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

xml-id

C5.S2.SS3.m1adec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5adec

0 references

Q11692

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C16.S1.XMD3.m1bdec

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

Wikipedia(0 entries)

DRMF related sites(0 entries)

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