DLMF:18.15.E12 (Q5704): Difference between revisions

From DRMF

Jump to navigation Jump to search

← Older edit

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
(5 intermediate revisions by the same user not shown)
		Property / Symbols used
			Q10754
		Property / Symbols used: Q10754 / rank
			Normal rank
		Property / Symbols used: Q10754 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}$ \binom{\NVar{m}}{\NVar{n}}
		Property / Symbols used: Q10754 / qualifier
			xml-id: C1.S2.SS1.m1adec
		Property / Symbols used
			cosine function
		Property / Symbols used: cosine function / rank
			Normal rank
		Property / Symbols used: cosine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\cos\NVar{z}}}$ \cos@@{\NVar{z}}
		Property / Symbols used: cosine function / qualifier
			xml-id: C4.S14.E2.m2addec
		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.m2addec
		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.m1hdec
		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.m1gdec
		Property / Symbols used
			DLMF:18.15.E13
		Property / Symbols used: DLMF:18.15.E13 / rank
			Normal rank
		Property / Symbols used: DLMF:18.15.E13 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\alpha_{n,m}}}$ \alpha_{n,m}
		Property / Symbols used: DLMF:18.15.E13 / qualifier
			xml-id: C18.S15.XMD10.m1dec

---

Latest revision as of 15:38, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:18.15.E12	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle P_{n}\left(\cos\theta\right)=\left(\frac{2}{\sin\theta}\right)^{\frac{1}{2}}\sum_{m=0}^{M-1}\genfrac{(}{)}{0.0pt}{}{-\tfrac{1}{2}}{m}\genfrac{(}{)}{0.0pt}{}{m-\frac{1}{2}}{n}\frac{\cos\alpha_{n,m}}{(2\sin\theta)^{m}}+O\left(\frac{1}{n^{M+\frac{1}{2}}}\right),}}$

0 references

DLMF id

DLMF:18.15.E12

0 references

Symbols used

order not exceeding

Defining formula

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

xml-id

C2.S1.E3.m2acdec

0 references

Q10920

Defining formula

${\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}$

xml-id

C18.S3.T1.t1.r10.m2adec

0 references

Q10754

Defining formula

${\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}$

xml-id

C1.S2.SS1.m1adec

0 references

cosine function

Defining formula

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

xml-id

C4.S14.E2.m2addec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2addec

0 references

Q11730

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C18.S1.XMD5.m1hdec

0 references

Q11726

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C18.S1.XMD6.m1gdec

0 references

DLMF:18.15.E13

Defining formula

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

xml-id

C18.S15.XMD10.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5704&oldid=59556"