DLMF:10.20.E4 (Q3253)

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Language	Label	Description	Also known as
English	DLMF:10.20.E4	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle J_{\nu}\left(\nu z\right)\sim\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}}}\sum_{k=0}^{\infty}\frac{A_{k}(\zeta)}{\nu^{2k% }}+\frac{\mathrm{Ai}'\left(\nu^{\frac{2}{3}}\zeta\right)}{\nu^{\frac{5}{3}}}% \sum_{k=0}^{\infty}\frac{B_{k}(\zeta)}{\nu^{2k}}\right),}}

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DLMF:10.20.E4

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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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Defining formula

{\displaystyle{\displaystyle\sim}}

C2.S1.SS3.p1.m11adec

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Defining formula

{\displaystyle{\displaystyle k}}

C10.S1.XMD3.m1dec

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Defining formula

{\displaystyle{\displaystyle z}}

C10.S1.XMD6.m1cdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1dec

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Defining formula

{\displaystyle{\displaystyle\zeta(z)}}

C10.S20.XMD1.m1cdec

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coefficients (locally)

Defining formula

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

C10.S20.XMD4.m1dec

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Sitelinks

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