DLMF:18.15.E22 (Q5717): Difference between revisions

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Revision as of 15:40, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 15:40, 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
			Q11759
		Property / Symbols used: Q11759 / rank
			Normal rank
		Property / Symbols used: Q11759 / qualifier
			Defining formula: ${\displaystyle{\displaystyle E_{m}}}$ E_{m}
		Property / Symbols used: Q11759 / qualifier
			xml-id: C18.S15.XMD19.m1dec
		Property / Symbols used
			coefficient (locally)
		Property / Symbols used: coefficient (locally) / rank
			Normal rank
		Property / Symbols used: coefficient (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle F_{m}}}$ F_{m}
		Property / Symbols used: coefficient (locally) / qualifier
			xml-id: C18.S15.XMD20.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.m1gdec

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Latest revision as of 15:40, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:18.15.E22	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle L^{(\alpha)}_{n}\left(\nu x\right)=(-1)^{n}\frac{e^{\frac{1}{2}\nu x}}{2^{\alpha-\frac{1}{2}}x^{\frac{1}{2}\alpha+\frac{1}{4}}}\*\left(\frac{\zeta}{x-1}\right)^{\frac{1}{4}}\left(\frac{\mathrm{Ai}\left(\nu^{\frac{2}{3}}\zeta\right)}{\nu^{\frac{1}{3}}}\sum_{m=0}^{M-1}\frac{E_{m}(\zeta)}{\nu^{2m}}+\frac{\mathrm{Ai}'\left(\nu^{\frac{2}{3}}\zeta\right)}{\nu^{\frac{5}{3}}}\sum_{m=0}^{M-1}\frac{F_{m}(\zeta)}{\nu^{2m}}+\mathrm{envAi}\left(\nu^{\frac{2}{3}}\zeta\right)O\left(\frac{1}{\nu^{2M-\frac{2}{3}}}\right)\right),}}$

0 references

DLMF id

DLMF:18.15.E22

0 references

Symbols used

Q10919

Defining formula

${\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}$

xml-id

C9.S2.SS1.m1adec

0 references

order not exceeding

Defining formula

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

xml-id

C2.S1.E3.m2afdec

0 references

Q11333

Defining formula

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

xml-id

C18.S3.T1.t1.r12.m2abdec

0 references

Q10931

Defining formula

${\displaystyle{\displaystyle\sim}}$

xml-id

C2.S1.SS3.p1.m11adec

0 references

Q11082

Defining formula

${\displaystyle{\displaystyle\mathrm{envAi}\left(\NVar{x}\right)}}$

xml-id

C2.S8.SS3.p4.m4adec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2abdec

0 references

Q11730

Defining formula

${\displaystyle{\displaystyle m}}$

xml-id

C18.S1.XMD5.m1ndec

0 references

Q11726

Defining formula

${\displaystyle{\displaystyle n}}$

xml-id

C18.S1.XMD6.m1mdec

0 references

DLMF:18.15.E17

Defining formula

${\displaystyle{\displaystyle\nu}}$

xml-id

C18.S15.XMD14.m1bdec

0 references

Q11758

Defining formula

${\displaystyle{\displaystyle\zeta}}$

xml-id

C18.S15.XMD18.m1adec

0 references

Q11759

Defining formula

${\displaystyle{\displaystyle E_{m}}}$

xml-id

C18.S15.XMD19.m1dec

0 references

coefficient (locally)

Defining formula

${\displaystyle{\displaystyle F_{m}}}$

xml-id

C18.S15.XMD20.m1dec

0 references

Q11727

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C18.S2.XMD3.m1gdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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