DLMF:31.10.E11 (Q9062): Difference between revisions

From DRMF

Jump to navigation Jump to search

← Older edit

Revision as of 13:37, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:37, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
(7 intermediate revisions by the same user not shown)
		Property / Symbols used
			Q12458
		Property / Symbols used: Q12458 / rank
			Normal rank
		Property / Symbols used: Q12458 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\gamma}}$ \gamma
		Property / Symbols used: Q12458 / qualifier
			xml-id: C31.S1.XMD10.m1fdec
		Property / Symbols used
			Q12459
		Property / Symbols used: Q12459 / rank
			Normal rank
		Property / Symbols used: Q12459 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\delta}}$ \delta
		Property / Symbols used: Q12459 / qualifier
			xml-id: C31.S1.XMD11.m1fdec
		Property / Symbols used
			Q12460
		Property / Symbols used: Q12460 / rank
			Normal rank
		Property / Symbols used: Q12460 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\epsilon}}$ \epsilon
		Property / Symbols used: Q12460 / qualifier
			xml-id: C31.S1.XMD12.m1fdec
		Property / Symbols used
			Q12461
		Property / Symbols used: Q12461 / rank
			Normal rank
		Property / Symbols used: Q12461 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a}}$ a
		Property / Symbols used: Q12461 / qualifier
			xml-id: C31.S1.XMD6.m1edec
		Property / Symbols used
			Q12463
		Property / Symbols used: Q12463 / rank
			Normal rank
		Property / Symbols used: Q12463 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\alpha}}$ \alpha
		Property / Symbols used: Q12463 / qualifier
			xml-id: C31.S1.XMD8.m1ddec
		Property / Symbols used
			Q12464
		Property / Symbols used: Q12464 / rank
			Normal rank
		Property / Symbols used: Q12464 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\beta}}$ \beta
		Property / Symbols used: Q12464 / qualifier
			xml-id: C31.S1.XMD9.m1ddec
		Property / Symbols used
			kernel (locally)
		Property / Symbols used: kernel (locally) / rank
			Normal rank
		Property / Symbols used: kernel (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathcal{K}(z,t)}}$ \mathcal{K}(z,t)
		Property / Symbols used: kernel (locally) / qualifier
			xml-id: C31.S10.XMD4.m1fdec
		Property / Symbols used
			Q12497
		Property / Symbols used: Q12497 / rank
			Normal rank
		Property / Symbols used: Q12497 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sigma}}$ \sigma
		Property / Symbols used: Q12497 / qualifier
			xml-id: C31.S10.XMD8.m1bdec

---

Latest revision as of 13:37, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:31.10.E11	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\mathcal{K}(z,t)=(zt-a)^{\frac{1}{2}-\delta-\sigma}\left(\ifrac{zt}{a}\right)^{-\frac{1}{2}+\delta+\sigma-\alpha}\*{{}_{2}F_{1}}\left({\frac{1}{2}-\delta-\sigma+\alpha,\frac{3}{2}-\delta-\sigma+\alpha-\gamma\atop\alpha-\beta+1};\frac{a}{zt}\right)\*P\begin{Bmatrix}0&1&\infty&\\ 0&0&-\frac{1}{2}+\delta+\sigma&\dfrac{(z-a)(t-a)}{(1-a)(zt-a)}\\ 1-\epsilon&1-\delta&-\frac{1}{2}+\epsilon-\sigma&\end{Bmatrix}.}}$

0 references

DLMF id

DLMF:31.10.E11

0 references

Symbols used

Q11581

Defining formula

${\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$

xml-id

C16.S2.m5aadec

0 references

Riemann’s $$P$$ -symbol for solutions of the generalized hypergeometric differential equation

Defining formula

${\displaystyle{\displaystyle P\NVar{\begin{Bmatrix}\alpha&\beta&\gamma&\\ a_{1}&b_{1}&c_{1}&z\\ a_{2}&b_{2}&c_{2}&\end{Bmatrix}}}}$

xml-id

C15.S11.E3.m2aadec

0 references

Q12457

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C31.S1.XMD1.m1edec

0 references

Q12458

Defining formula

${\displaystyle{\displaystyle\gamma}}$

xml-id

C31.S1.XMD10.m1fdec

0 references

Q12459

Defining formula

${\displaystyle{\displaystyle\delta}}$

xml-id

C31.S1.XMD11.m1fdec

0 references

Q12460

Defining formula

${\displaystyle{\displaystyle\epsilon}}$

xml-id

C31.S1.XMD12.m1fdec

0 references

Q12461

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C31.S1.XMD6.m1edec

0 references

Q12463

Defining formula

${\displaystyle{\displaystyle\alpha}}$

xml-id

C31.S1.XMD8.m1ddec

0 references

Q12464

Defining formula

${\displaystyle{\displaystyle\beta}}$

xml-id

C31.S1.XMD9.m1ddec

0 references

kernel (locally)

Defining formula

${\displaystyle{\displaystyle\mathcal{K}(z,t)}}$

xml-id

C31.S10.XMD4.m1fdec

0 references

Q12497

Defining formula

${\displaystyle{\displaystyle\sigma}}$

xml-id

C31.S10.XMD8.m1bdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q9062&oldid=38333"