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We study the roots of the generalised Hermite polynomials H m,n when both m and n are large. We prove that the roots, when appropriately rescaled, densely fill a bounded… Click to show full abstract
We study the roots of the generalised Hermite polynomials H m,n when both m and n are large. We prove that the roots, when appropriately rescaled, densely fill a bounded quadrilateral region, called the elliptic region, and organise themselves on a deformed rectangular grid, as was numerically observed by Clarkson. We describe the elliptic region and the deformed grid in terms of elliptic integrals and their degenerations.
Keywords:
generalised hermite;
parameters large;
hermite polynomials;
roots generalised;
polynomials parameters;
region
Journal Title: Nonlinearity
Year Published: 2019
Link to full text (if available)
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Journal Title: Nonlinearity
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!