DLMF:10.41.E14 (Q3611)

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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),}}

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DLMF:10.41.E14

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Defining formula

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

C9.S2.SS1.m1adec

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Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2adec

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order not exceeding

Defining formula

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

C2.S1.E3.m2abdec

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Defining formula

{\displaystyle{\displaystyle k}}

C10.S1.XMD3.m1hdec

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