DLMF:18.15.E10 (Q5702): Difference between revisions

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Revision as of 15:38, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:38, 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
			Q11730
		Property / Symbols used: Q11730 / rank
			Normal rank
		Property / Symbols used: Q11730 / qualifier
			Defining formula: ${\displaystyle{\displaystyle m}}$ m
		Property / Symbols used: Q11730 / qualifier
			xml-id: C18.S1.XMD5.m1fdec
		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.m1edec
		Property / Symbols used
			DLMF:18.15.E11
		Property / Symbols used: DLMF:18.15.E11 / rank
			Normal rank
		Property / Symbols used: DLMF:18.15.E11 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\theta_{n,m}}}$ \theta_{n,m}
		Property / Symbols used: DLMF:18.15.E11 / qualifier
			xml-id: C18.S15.XMD9.m1dec

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Latest revision as of 15:38, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:18.15.E10	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle C^{(\lambda)}_{n}\left(\cos\theta\right)=\frac{2^{2\lambda}\Gamma\left(\lambda+\frac{1}{2}\right)}{\pi^{\frac{1}{2}}\Gamma\left(\lambda+1\right)}\frac{{\left(2\lambda\right)_{n}}}{{\left(\lambda+1\right)_{n}}}\*\left(\sum_{m=0}^{M-1}\dfrac{{\left(\lambda\right)_{m}}{\left(1-\lambda\right)_{m}}}{m!\,{\left(n+\lambda+1\right)_{m}}}\dfrac{\cos\theta_{n,m}}{(2\sin\theta)^{m+\lambda}}+O\left(\frac{1}{n^{M}}\right)\right),}}$

0 references

DLMF id

DLMF:18.15.E10

0 references

Symbols used

order not exceeding

Defining formula

${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$

xml-id

C2.S1.E3.m2abdec

0 references

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2aadec

0 references

Q10759

Defining formula

${\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}$

xml-id

C5.S2.SS3.m1abdec

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

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5abdec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2acdec

0 references

Q11475

Defining formula

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

xml-id

C18.S3.T1.t1.r3.m2adec

0 references

Q11730

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C18.S1.XMD5.m1fdec

0 references

Q11726

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C18.S1.XMD6.m1edec

0 references

DLMF:18.15.E11

Defining formula

${\displaystyle{\displaystyle\theta_{n,m}}}$

xml-id

C18.S15.XMD9.m1dec

0 references

 

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