DLMF:15.6.E7 (Q5045): Difference between revisions

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Revision as of 13:58, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:58, 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
			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.m1fdec
		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.m1fdec

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Latest revision as of 13:58, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:15.6.E7	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\mathbf{F}\left(a,b;c;z\right)=\frac{1}{2\pi\mathrm{i}\Gamma\left(a\right)\Gamma\left(b\right)\Gamma\left(c-a\right)\Gamma\left(c-b\right)}\int_{-\mathrm{i}\infty}^{\mathrm{i}\infty}\Gamma\left(a+t\right)\Gamma\left(b+t\right)\Gamma\left(c-a-b-t\right)\Gamma\left(-t\right)(1-z)^{t}\mathrm{d}t,}}$

0 references

DLMF id

DLMF:15.6.E7

0 references

constraint

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

0 references

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

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${\displaystyle{\displaystyle a,b,c-a,c-b\neq 0,-1,-2,\dots}}$

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2afdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2afdec

0 references

Q10770

Defining formula

${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$

xml-id

C1.S4.SS4.m1afdec

0 references

imaginary unit

Defining formula

${\displaystyle{\displaystyle\mathrm{i}}}$

xml-id

C1.S9.E1.m2aedec

0 references

Q10771

Defining formula

${\displaystyle{\displaystyle\int}}$

xml-id

C1.S4.SS4.m3afdec

0 references

Q10817

Defining formula

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

xml-id

C1.S9.E7.m1afdec

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.m2afdec

0 references

Q11644

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C15.S1.XMD3.m1fdec

0 references

Q11645

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C15.S1.XMD4.m1fdec

0 references

Q11646

Defining formula

${\displaystyle{\displaystyle b}}$

xml-id

C15.S1.XMD5.m1fdec

0 references

Q11647

Defining formula

${\displaystyle{\displaystyle c}}$

xml-id

C15.S1.XMD6.m1fdec

0 references

 

Sitelinks

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