DLMF:18.11.E5 (Q5639)

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Language	Label	Description	Also known as
English	DLMF:18.11.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\lim_{n\to\infty}\frac{1}{n^{\alpha}}P^{(\alpha,% \beta)}_{n}\left(1-\frac{z^{2}}{2n^{2}}\right)=\lim_{n\to\infty}\frac{1}{n^{% \alpha}}P^{(\alpha,\beta)}_{n}\left(\cos\frac{z}{n}\right)=\frac{2^{\alpha}}{z% ^{\alpha}}J_{\alpha}\left(z\right).}}

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DLMF:18.11.E5

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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 P^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{n}}\left(% \NVar{x}\right)}}

C18.S3.T1.t1.r2.m2aadec

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cosine function

Defining formula

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

C4.S14.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle z}}

C18.S1.XMD2.m1dec

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Sitelinks

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