Formula:KLS:09.03:29

<< Formula:KLS:09.03:28

formula in Continuous dual Hahn

Formula:KLS:09.04:01 >>

${\displaystyle{\displaystyle{\displaystyle\frac{|S_{n}\!\left(-a^{2};a,b,c\right)|^{2}}{h_{n}}=O(n^{2\Re{a}-1})\hbox{as $n\to\infty$.}}}}$

Proof

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Symbols List

${\displaystyle{\displaystyle{\displaystyle S_{n}}}}$ : continuous dual Hahn polynomial : http://dlmf.nist.gov/18.25#T1.t1.r3
${\displaystyle{\displaystyle{\displaystyle\Re{z}}}}$ : real part : http://dlmf.nist.gov/1.9#E2

Bibliography

Equation in Section 9.3 of KLS.

URL links

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formula in Continuous dual Hahn

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