DLMF:15.8.E11 (Q5068): Difference between revisions

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Revision as of 14:03, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 14:03, 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.m1hdec
		Property / Symbols used
			Q11658
		Property / Symbols used: Q11658 / rank
			Normal rank
		Property / Symbols used: Q11658 / qualifier
			Defining formula: ${\displaystyle{\displaystyle k}}$ k
		Property / Symbols used: Q11658 / qualifier
			xml-id: C15.S1.XMD7.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.m1edec

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Latest revision as of 14:03, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:15.8.E11	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop a+b+m};z\right)=\frac{z^{-a}}{\Gamma\left(a+m\right)}\sum_{k=0}^{m-1}\frac{(a)_{k}(m-k-1)!}{k!\Gamma\left(b+m-k\right)}\left(1-\frac{1}{z}\right)^{k}-\frac{z^{-a}}{\Gamma\left(a\right)}\sum_{k=0}^{\infty}\frac{(a+m)_{k}}{k!(k+m)!\Gamma\left(b-k\right)}(-1)^{k}\left(1-\frac{1}{z}\right)^{k+m}\*\left(\ln\left(\frac{1-z}{z}\right)-\psi\left(k+1\right)-\psi\left(k+m+1\right)+\psi\left(a+k+m\right)+\psi\left(b-k\right)\right),}}$

0 references

DLMF id

DLMF:15.8.E11

0 references

constraint

${\displaystyle{\displaystyle\Re z>\tfrac{1}{2},|\operatorname{ph}z|<\pi,|\operatorname{ph}\left(1-z\right)|<\pi}}$

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2agdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2ahdec

0 references

psi (or digamma) function

Defining formula

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

xml-id

C5.S2.E2.m2acdec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5acdec

0 references

principal branch of logarithm function

Defining formula

${\displaystyle{\displaystyle\ln\NVar{z}}}$

xml-id

C4.S2.E2.m2acdec

0 references

Q10817

Defining formula

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

xml-id

C1.S9.E7.m1ahdec

0 references

Q10811

Defining formula

${\displaystyle{\displaystyle\Re}}$

xml-id

C1.S9.E2.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.m2ahdec

0 references

Q11644

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C15.S1.XMD3.m1jdec

0 references

Q11645

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C15.S1.XMD4.m1hdec

0 references

Q11646

Defining formula

${\displaystyle{\displaystyle b}}$

xml-id

C15.S1.XMD5.m1hdec

0 references

Q11658

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C15.S1.XMD7.m1cdec

0 references

Q11651

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C15.S1.XMD9.m1edec

0 references

 

Sitelinks

Wikipedia(0 entries)

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