DLMF:15.8.E25 (Q5082): Difference between revisions

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		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.m1wdec
		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.m1tdec

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Latest revision as of 14:06, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:15.8.E25	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle F\left({a,b\atop\tfrac{1}{2}(a+b+1)};z\right)=\frac{\Gamma\left(\tfrac{1}{2}(a+b+1)\right)\Gamma\left(\tfrac{1}{2}\right)}{\Gamma\left(\tfrac{1}{2}a+\tfrac{1}{2}\right)\Gamma\left(\tfrac{1}{2}b+\tfrac{1}{2}\right)}F\left({\tfrac{1}{2}a,\tfrac{1}{2}b\atop\tfrac{1}{2}};(1-2z)^{2}\right)+(1-2z)\frac{\Gamma\left(\tfrac{1}{2}(a+b+1)\right)\Gamma\left(-\tfrac{1}{2}\right)}{\Gamma\left(\tfrac{1}{2}a\right)\Gamma\left(\tfrac{1}{2}b\right)}F\left({\tfrac{1}{2}a+\tfrac{1}{2},\tfrac{1}{2}b+\tfrac{1}{2}\atop\tfrac{3}{2}};(1-2z)^{2}\right),}}$

0 references

DLMF id

DLMF:15.8.E25

0 references

constraint

${\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}$

0 references

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

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Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2aidec

0 references

$$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function

Defining formula

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

xml-id

C15.S2.E1.m2andec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2aodec

0 references

Q10817

Defining formula

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

xml-id

C1.S9.E7.m1aodec

0 references

Q11644

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C15.S1.XMD3.m1xdec

0 references

Q11645

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C15.S1.XMD4.m1wdec

0 references

Q11646

Defining formula

${\displaystyle{\displaystyle b}}$

xml-id

C15.S1.XMD5.m1tdec

0 references

 

Sitelinks

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