DLMF:18.10.E4 (Q5628): Difference between revisions

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Revision as of 15:26, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:27, 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
			imaginary unit
		Property / Symbols used: imaginary unit / rank
			Normal rank
		Property / Symbols used: imaginary unit / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{i}}}$ \iunit
		Property / Symbols used: imaginary unit / qualifier
			xml-id: C1.S9.E1.m2aadec
		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.m3acdec
		Property / Symbols used
			sine function
		Property / Symbols used: sine function / rank
			Normal rank
		Property / Symbols used: sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sin\NVar{z}}}$ \sin@@{\NVar{z}}
		Property / Symbols used: sine function / qualifier
			xml-id: C4.S14.E1.m2abdec
		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.m2aadec
		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.m1cdec

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Latest revision as of 15:27, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:18.10.E4	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle{\frac{P^{(\alpha,\alpha)}_{n}\left(\cos\theta\right)}{P^{(\alpha,\alpha)}_{n}\left(1\right)}=\frac{C^{(\alpha+\frac{1}{2})}_{n}\left(\cos\theta\right)}{C^{(\alpha+\frac{1}{2})}_{n}\left(1\right)}}=\frac{\Gamma\left(\alpha+1\right)}{\pi^{\frac{1}{2}}\Gamma{(\alpha+\tfrac{1}{2})}}\*{\int_{0}^{\pi}(\cos\theta+i\sin\theta\cos\phi)^{n}\*(\sin\phi)^{2\alpha}\mathrm{d}\phi},}}$

0 references

DLMF id

DLMF:18.10.E4

0 references

constraint

${\displaystyle{\displaystyle\alpha>-\frac{1}{2}}}$

0 references

Symbols used

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2abdec

0 references

Q11660

Defining formula

${\displaystyle{\displaystyle P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(\NVar{x}\right)}}$

xml-id

C18.S3.T1.t1.r2.m2abdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2acdec

0 references

cosine function

Defining formula

${\displaystyle{\displaystyle\cos\NVar{z}}}$

xml-id

C4.S14.E2.m2acdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1acdec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2aadec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3acdec

0 references

sine function

Defining formula

${\displaystyle{\displaystyle\sin\NVar{z}}}$

xml-id

C4.S14.E1.m2abdec

0 references

Q11475

Defining formula

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

xml-id

C18.S3.T1.t1.r3.m2aadec

0 references

Q11726

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C18.S1.XMD6.m1cdec

0 references

 

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