DLMF:15.2.E4 (Q4981): Difference between revisions

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Revision as of 13:46, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:46, 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
			Q10754
		Property / Symbols used: Q10754 / rank
			Normal rank
		Property / Symbols used: Q10754 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}$ \binom{\NVar{m}}{\NVar{n}}
		Property / Symbols used: Q10754 / qualifier
			xml-id: C1.S2.SS1.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.m5abdec
		Property / Symbols used
			Q11650
		Property / Symbols used: Q11650 / rank
			Normal rank
		Property / Symbols used: Q11650 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11650 / qualifier
			xml-id: C15.S1.XMD10.m1dec
		Property / Symbols used
			Q11644
		Property / Symbols used: Q11644 / rank
			Normal rank
		Property / Symbols used: Q11644 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11644 / qualifier
			xml-id: C15.S1.XMD3.m1bdec
		Property / Symbols used
			Q11646
		Property / Symbols used: Q11646 / rank
			Normal rank
		Property / Symbols used: Q11646 / qualifier
			Defining formula: ${\displaystyle{\displaystyle b}}$ b
		Property / Symbols used: Q11646 / qualifier
			xml-id: C15.S1.XMD5.m1cdec
		Property / Symbols used
			Q11647
		Property / Symbols used: Q11647 / rank
			Normal rank
		Property / Symbols used: Q11647 / qualifier
			Defining formula: ${\displaystyle{\displaystyle c}}$ c
		Property / Symbols used: Q11647 / qualifier
			xml-id: C15.S1.XMD6.m1cdec
		Property / Symbols used
			Q11651
		Property / Symbols used: Q11651 / rank
			Normal rank
		Property / Symbols used: Q11651 / qualifier
			Defining formula: ${\displaystyle{\displaystyle m}}$ m
		Property / Symbols used: Q11651 / qualifier
			xml-id: C15.S1.XMD9.m1dec

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Latest revision as of 13:46, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:15.2.E4	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle F\left(-m,b;c;z\right)=\sum_{n=0}^{m}\frac{{\left(-m\right)_{n}}{\left(b\right)_{n}}}{{\left(c\right)_{n}}{n!}}z^{n}=\sum_{n=0}^{m}(-1)^{n}\genfrac{(}{)}{0.0pt}{}{m}{n}\frac{{\left(b\right)_{n}}}{{\left(c\right)_{n}}}z^{n}.}}$

0 references

DLMF id

DLMF:15.2.E4

0 references

Symbols used

$$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function

Defining formula

${\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$

xml-id

C15.S2.E1.m2aadec

0 references

Q10759

Defining formula

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

xml-id

C5.S2.SS3.m1abdec

0 references

Q10754

Defining formula

${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}$

xml-id

C1.S2.SS1.m1adec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5abdec

0 references

Q11650

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C15.S1.XMD10.m1dec

0 references

Q11644

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C15.S1.XMD3.m1bdec

0 references

Q11646

Defining formula

${\displaystyle{\displaystyle b}}$

xml-id

C15.S1.XMD5.m1cdec

0 references

Q11647

Defining formula

${\displaystyle{\displaystyle c}}$

xml-id

C15.S1.XMD6.m1cdec

0 references

Q11651

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C15.S1.XMD9.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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