DLMF:10.41.E14 (Q3611): Difference between revisions

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Revision as of 13:58, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 13:58, 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
			coefficients (locally)
		Property / Symbols used: coefficients (locally) / rank
			Normal rank
		Property / Symbols used: coefficients (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle A_{k}(\zeta)}}$ A_{k}(\zeta)
		Property / Symbols used: coefficients (locally) / qualifier
			xml-id: C10.S20.XMD4.m1dec
		Property / Symbols used
			coefficients (locally)
		Property / Symbols used: coefficients (locally) / rank
			Normal rank
		Property / Symbols used: coefficients (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle B_{k}(\zeta)}}$ B_{k}(\zeta)
		Property / Symbols used: coefficients (locally) / qualifier
			xml-id: C10.S20.XMD5.m1dec

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Latest revision as of 13:58, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.41.E14	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle J_{\nu}\left(\nu z\right)=\left(\frac{4\zeta}{1-z^{2}}\right)^{\frac{1}{4}}\left(\frac{\mathrm{Ai}\left(\nu^{\frac{2}{3}}\zeta\right)}{\nu^{\frac{1}{3}}}\left(\sum_{k=0}^{\ell}\frac{A_{k}(\zeta)}{\nu^{2k}}+O\left(\frac{1}{\zeta^{3\ell+3}}\right)\right)+\frac{\mathrm{Ai}'\left(\nu^{\frac{2}{3}}\zeta\right)}{\nu^{\frac{5}{3}}}\left(\sum_{k=0}^{\ell-1}\frac{B_{k}(\zeta)}{\nu^{2k}}+O\left(\frac{1}{\zeta^{3\ell+1}}\right)\right)\right),}}$

0 references

DLMF id

DLMF:10.41.E14

0 references

Symbols used

Q10919

Defining formula

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

xml-id

C9.S2.SS1.m1adec

0 references

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

order not exceeding

Defining formula

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

xml-id

C2.S1.E3.m2abdec

0 references

Q11428

Defining formula

${\displaystyle{\displaystyle k}}$

xml-id

C10.S1.XMD3.m1hdec

0 references

Q11426

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C10.S1.XMD6.m1kdec

0 references

Q11427

Defining formula

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

xml-id

C10.S1.XMD7.m1hdec

0 references

coefficients (locally)

Defining formula

${\displaystyle{\displaystyle A_{k}(\zeta)}}$

xml-id

C10.S20.XMD4.m1dec

0 references

coefficients (locally)

Defining formula

${\displaystyle{\displaystyle B_{k}(\zeta)}}$

xml-id

C10.S20.XMD5.m1dec

0 references

 

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