DLMF:18.17.E37 (Q5778): Difference between revisions

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Revision as of 01:17, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 01:18, 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
			Q10771
		Property / Symbols used: Q10771 / rank
			Normal rank
		Property / Symbols used: Q10771 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\int}}$ \int
		Property / Symbols used: Q10771 / qualifier
			xml-id: C1.S4.SS4.m3aajdec
		Property / Symbols used
			Q10811
		Property / Symbols used: Q10811 / rank
			Normal rank
		Property / Symbols used: Q10811 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\Re}}$ \realpart@@
		Property / Symbols used: Q10811 / qualifier
			xml-id: C1.S9.E2.m1abdec
		Property / Symbols used
			Q11475
		Property / Symbols used: Q11475 / rank
			Normal rank
		Property / Symbols used: Q11475 / qualifier
			Defining formula: ${\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}\right)}}$ \ultrasphpoly{\NVar{\lambda}}{\NVar{n}}@{\NVar{x}}
		Property / Symbols used: Q11475 / qualifier
			xml-id: C18.S3.T1.t1.r3.m2aedec
		Property / Symbols used
			Q11750
		Property / Symbols used: Q11750 / rank
			Normal rank
		Property / Symbols used: Q11750 / qualifier
			Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11750 / qualifier
			xml-id: C18.S1.XMD2.m1ddec
		Property / Symbols used
			Q11726
		Property / Symbols used: Q11726 / rank
			Normal rank
		Property / Symbols used: Q11726 / qualifier
			Defining formula: ${\displaystyle{\displaystyle n}}$ n
		Property / Symbols used: Q11726 / qualifier
			xml-id: C18.S1.XMD6.m1ajdec
		Property / Symbols used
			Q11727
		Property / Symbols used: Q11727 / rank
			Normal rank
		Property / Symbols used: Q11727 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11727 / qualifier
			xml-id: C18.S2.XMD3.m1ahdec

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Latest revision as of 01:18, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:18.17.E37	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{0}^{1}(1-x^{2})^{\lambda-\frac{1}{2}}C^{(\lambda)}_{n}\left(x\right)x^{z-1}\mathrm{d}x=\frac{\pi\,2^{1-2\lambda-z}\Gamma\left(n+2\lambda\right)\Gamma\left(z\right)}{n!\Gamma\left(\lambda\right)\Gamma\left(\frac{1}{2}+\frac{1}{2}n+\lambda+\frac{1}{2}z\right)\Gamma\left(\frac{1}{2}+\frac{1}{2}z-\frac{1}{2}n\right)},}}$

0 references

DLMF id

DLMF:18.17.E37

0 references

constraint

${\displaystyle{\displaystyle\Re z>0}}$

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2aodec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2asdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1aajdec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5aldec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3aajdec

0 references

Q10811

Defining formula

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

xml-id

C1.S9.E2.m1abdec

0 references

Q11475

Defining formula

${\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}\right)}}$

xml-id

C18.S3.T1.t1.r3.m2aedec

0 references

Q11750

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C18.S1.XMD2.m1ddec

0 references

Q11726

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C18.S1.XMD6.m1ajdec

0 references

Q11727

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C18.S2.XMD3.m1ahdec

0 references

 

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