DLMF:14.3.E19 (Q4708): Difference between revisions

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Revision as of 01:19, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 01:19, 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
			Q11592
		Property / Symbols used: Q11592 / rank
			Normal rank
		Property / Symbols used: Q11592 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$ \assLegendreOlverQ[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}}
		Property / Symbols used: Q11592 / qualifier
			xml-id: C14.S21.SS1.p1.m3aadec
		Property / Symbols used
			$$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function
		Property / Symbols used: $$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function / rank
			Normal rank
		Property / Symbols used: $$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$ \hyperOlverF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}
		Property / Symbols used: $$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function / qualifier
			xml-id: C15.S2.E2.m2aodec
		Property / Symbols used
			Q11589
		Property / Symbols used: Q11589 / rank
			Normal rank
		Property / Symbols used: Q11589 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11589 / qualifier
			xml-id: C14.S1.XMD1.m1rdec
		Property / Symbols used
			Q11591
		Property / Symbols used: Q11591 / rank
			Normal rank
		Property / Symbols used: Q11591 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mu}}$ \mu
		Property / Symbols used: Q11591 / qualifier
			xml-id: C14.S1.XMD7.m1ndec
		Property / Symbols used
			Q11590
		Property / Symbols used: Q11590 / rank
			Normal rank
		Property / Symbols used: Q11590 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\nu}}$ \nu
		Property / Symbols used: Q11590 / qualifier
			xml-id: C14.S1.XMD8.m1qdec

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Latest revision as of 01:19, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:14.3.E19	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu}\left(x\right)=\frac{2^{\nu}\Gamma\left(\nu+1\right)(x+1)^{\mu/2}}{(x-1)^{(\mu/2)+\nu+1}}\mathbf{F}\left(\nu+1,\nu+\mu+1;2\nu+2;\frac{2}{1-x}\right),}}$

0 references

DLMF id

DLMF:14.3.E19

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2akdec

0 references

Q11592

Defining formula

${\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C14.S21.SS1.p1.m3aadec

0 references

$$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function

Defining formula

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

xml-id

C15.S2.E2.m2aodec

0 references

Q11589

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C14.S1.XMD1.m1rdec

0 references

Q11591

Defining formula

${\displaystyle{\displaystyle\mu}}$

xml-id

C14.S1.XMD7.m1ndec

0 references

Q11590

Defining formula

${\displaystyle{\displaystyle\nu}}$

xml-id

C14.S1.XMD8.m1qdec

0 references

 

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