Formula:KLS:09.13:16

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formula in Bessel

Formula:KLS:09.14:01 >>

${\displaystyle{\displaystyle{\displaystyle\lim\limits_{\nu\rightarrow\infty}\frac{P_{n}\!\left(\nu x;\nu,N\right)}{\nu^{n}}=\frac{2^{n}}{{\left(n-2N-1\right)_{n}}}y_{n}\!\left(x;-2N-2\right)}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle P_{n}}}}$ : pseudo Jacobi polynomomal : http://drmf.wmflabs.org/wiki/Definition:pseudoJacobi
${\displaystyle{\displaystyle{\displaystyle(a)_{n}}}}$ : Pochhammer symbol : http://dlmf.nist.gov/5.2#iii
${\displaystyle{\displaystyle{\displaystyle y_{n}}}}$ : Bessel polynomial : http://dlmf.nist.gov/18.34#E1

Bibliography

Equation in Section 9.13 of KLS.

URL links

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