DLMF:18.15.E14 (Q5706): 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 15:39, 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
			the ratio of the circumference of a circle to its diameter
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
			Normal rank
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			Defining formula: ${\displaystyle{\displaystyle\pi}}$ \cpi
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			xml-id: C3.S12.E1.m2afdec
		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.m2aedec
		Property / Symbols used
			base of natural logarithm
		Property / Symbols used: base of natural logarithm / rank
			Normal rank
		Property / Symbols used: base of natural logarithm / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{e}}}$ \expe
		Property / Symbols used: base of natural logarithm / qualifier
			xml-id: C4.S2.E11.m2adec
		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.m2aedec
		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.m1jdec
		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.m1idec
		Property / Symbols used
			DLMF:18.15.E15
		Property / Symbols used: DLMF:18.15.E15 / rank
			Normal rank
		Property / Symbols used: DLMF:18.15.E15 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\theta_{n}^{(\alpha)}(x)}}$ \theta_{n}^{(\alpha)}(x)
		Property / Symbols used: DLMF:18.15.E15 / qualifier
			xml-id: C18.S15.XMD11.m1dec
		Property / Symbols used
			Q11755
		Property / Symbols used: Q11755 / rank
			Normal rank
		Property / Symbols used: Q11755 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a_{m}(x)}}$ a_{m}(x)
		Property / Symbols used: Q11755 / qualifier
			xml-id: C18.S15.XMD12.m1dec
		Property / Symbols used
			Q11756
		Property / Symbols used: Q11756 / rank
			Normal rank
		Property / Symbols used: Q11756 / qualifier
			Defining formula: ${\displaystyle{\displaystyle b_{m}(x)}}$ b_{m}(x)
		Property / Symbols used: Q11756 / qualifier
			xml-id: C18.S15.XMD13.m1dec
		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.m1dec

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Latest revision as of 15:39, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:18.15.E14	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle L^{(\alpha)}_{n}\left(x\right)=\frac{n^{\frac{1}{2}\alpha-\frac{1}{4}}e^{\frac{1}{2}x}}{\pi^{\frac{1}{2}}x^{\frac{1}{2}\alpha+\frac{1}{4}}}\left(\cos\theta_{n}^{(\alpha)}(x)\left(\sum_{m=0}^{M-1}\frac{a_{m}(x)}{n^{\frac{1}{2}m}}+O\left(\frac{1}{n^{\frac{1}{2}M}}\right)\right)+\sin\theta_{n}^{(\alpha)}(x)\left(\sum_{m=1}^{M-1}\frac{b_{m}(x)}{n^{\frac{1}{2}m}}+O\left(\frac{1}{n^{\frac{1}{2}M}}\right)\right)\right),}}$

0 references

DLMF id

DLMF:18.15.E14

0 references

Symbols used

order not exceeding

Defining formula

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

xml-id

C2.S1.E3.m2addec

0 references

Q11333

Defining formula

${\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}\right)}}$

xml-id

C18.S3.T1.t1.r12.m2adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2afdec

0 references

cosine function

Defining formula

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

xml-id

C4.S14.E2.m2aedec

0 references

base of natural logarithm

Defining formula

${\displaystyle{\displaystyle\mathrm{e}}}$

xml-id

C4.S2.E11.m2adec

0 references

sine function

Defining formula

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

xml-id

C4.S14.E1.m2aedec

0 references

Q11730

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C18.S1.XMD5.m1jdec

0 references

Q11726

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C18.S1.XMD6.m1idec

0 references

DLMF:18.15.E15

Defining formula

${\displaystyle{\displaystyle\theta_{n}^{(\alpha)}(x)}}$

xml-id

C18.S15.XMD11.m1dec

0 references

Q11755

Defining formula

${\displaystyle{\displaystyle a_{m}(x)}}$

xml-id

C18.S15.XMD12.m1dec

0 references

Q11756

Defining formula

${\displaystyle{\displaystyle b_{m}(x)}}$

xml-id

C18.S15.XMD13.m1dec

0 references

Q11727

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C18.S2.XMD3.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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