DLMF:15.9.E16 (Q5106): Difference between revisions

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Revision as of 14:10, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:10, 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
			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.m1adec
		Property / Symbols used
			Q11645
		Property / Symbols used: Q11645 / rank
			Normal rank
		Property / Symbols used: Q11645 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a}}$ a
		Property / Symbols used: Q11645 / qualifier
			xml-id: C15.S1.XMD4.m1dec
		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.m1dec

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Latest revision as of 14:10, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:15.9.E16	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop 2b};z\right)=\frac{\sqrt{\pi}}{\Gamma\left(b\right)}z^{-b+(\ifrac{1}{2})}(1-z)^{(b-a-(\ifrac{1}{2}))/2}\*P^{-b+(\ifrac{1}{2})}_{a-b-(\ifrac{1}{2})}\left(\frac{2-z}{2\sqrt{1-z}}\right),}}$

0 references

DLMF id

DLMF:15.9.E16

0 references

constraint

${\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}$

0 references

${\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}$

0 references

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

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2abdec

0 references

Q11481

Defining formula

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

xml-id

C14.S21.SS1.p1.m1adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

${\displaystyle{\displaystyle\pi}}$

xml-id

C3.S12.E1.m2aadec

0 references

Q10817

Defining formula

${\displaystyle{\displaystyle\operatorname{ph}}}$

xml-id

C1.S9.E7.m1adec

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.m2adec

0 references

Q11644

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C15.S1.XMD3.m1adec

0 references

Q11645

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C15.S1.XMD4.m1dec

0 references

Q11646

Defining formula

${\displaystyle{\displaystyle b}}$

xml-id

C15.S1.XMD5.m1dec

0 references

 

Sitelinks

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