DLMF:18.15.E6 (Q5696): Difference between revisions

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Revision as of 15:37, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:37, 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
			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
			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.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.m1ddec
		Property / Symbols used
			DLMF:18.15.E5
		Property / Symbols used: DLMF:18.15.E5 / rank
			Normal rank
		Property / Symbols used: DLMF:18.15.E5 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\rho}}$ \rho
		Property / Symbols used: DLMF:18.15.E5 / qualifier
			xml-id: C18.S15.XMD4.m1adec
		Property / Symbols used
			DLMF:18.15.E7
		Property / Symbols used: DLMF:18.15.E7 / rank
			Normal rank
		Property / Symbols used: DLMF:18.15.E7 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\varepsilon_{M}(\rho,\theta)}}$ \varepsilon_{M}(\rho,\theta)
		Property / Symbols used: DLMF:18.15.E7 / qualifier
			xml-id: C18.S15.XMD5.m1dec
		Property / Symbols used
			Q11752
		Property / Symbols used: Q11752 / rank
			Normal rank
		Property / Symbols used: Q11752 / qualifier
			Defining formula: ${\displaystyle{\displaystyle A_{m}(\theta)}}$ A_{m}(\theta)
		Property / Symbols used: Q11752 / qualifier
			xml-id: C18.S15.XMD6.m1dec
		Property / Symbols used
			Q11753
		Property / Symbols used: Q11753 / rank
			Normal rank
		Property / Symbols used: Q11753 / qualifier
			Defining formula: ${\displaystyle{\displaystyle B_{m}(\theta)}}$ B_{m}(\theta)
		Property / Symbols used: Q11753 / qualifier
			xml-id: C18.S15.XMD7.m1dec

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Latest revision as of 15:37, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:18.15.E6	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle(\sin\tfrac{1}{2}\theta)^{\alpha+\frac{1}{2}}(\cos\tfrac{1}{2}\theta)^{\beta+\frac{1}{2}}P^{(\alpha,\beta)}_{n}\left(\cos\theta\right)=\frac{\Gamma\left(n+\alpha+1\right)}{2^{\frac{1}{2}}\rho^{\alpha}n!}\*\left(\theta^{\frac{1}{2}}J_{\alpha}\left(\rho\theta\right)\sum_{m=0}^{M}\dfrac{A_{m}(\theta)}{\rho^{2m}}+\theta^{\frac{3}{2}}J_{\alpha+1}\left(\rho\theta\right)\sum_{m=0}^{M-1}\dfrac{B_{m}(\theta)}{\rho^{2m+1}}+\varepsilon_{M}(\rho,\theta)\right),}}$

0 references

DLMF id

DLMF:18.15.E6

0 references

Symbols used

Bessel function of the first kind

Defining formula

${\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}$

xml-id

C10.S2.E2.m2adec

0 references

gamma function

Defining formula

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

xml-id

C5.S2.E1.m2adec

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.m2aadec

0 references

cosine function

Defining formula

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

xml-id

C4.S14.E2.m2abdec

0 references

Q10755

Defining formula

${\displaystyle{\displaystyle!}}$

xml-id

introduction.Sx4.p1.t1.r15.m5aadec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2abdec

0 references

Q11730

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C18.S1.XMD5.m1ddec

0 references

Q11726

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C18.S1.XMD6.m1ddec

0 references

DLMF:18.15.E5

Defining formula

${\displaystyle{\displaystyle\rho}}$

xml-id

C18.S15.XMD4.m1adec

0 references

DLMF:18.15.E7

Defining formula

${\displaystyle{\displaystyle\varepsilon_{M}(\rho,\theta)}}$

xml-id

C18.S15.XMD5.m1dec

0 references

Q11752

Defining formula

${\displaystyle{\displaystyle A_{m}(\theta)}}$

xml-id

C18.S15.XMD6.m1dec

0 references

Q11753

Defining formula

${\displaystyle{\displaystyle B_{m}(\theta)}}$

xml-id

C18.S15.XMD7.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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