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Mark V. DeFazio - The behaviour of the complex zeroes of the Laguerre polynomial



MARK V. DEFAZIO, Department of Mathematics and Statistics, York University, Toronto, Ontario  M3J 1P3, Canada
The behaviour of the complex zeroes of the Laguerre polynomial


When $\alpha > -1$, the behaviour of the zeroes of $L_n^{(\alpha)}(x)$is well understood. There are n positive distinct real zeroes and they are continuously increasing functions of $\alpha$. When $\alpha <
-1$, these zeroes can be complex and their behaviour as $\alpha$ varies is not well known. I will present results on the location of the complex zeroes of $L_n^{(\alpha)}(z)$ and describe their behaviour as $\alpha <
-1$ varies.



 

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