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Miklós Schweitzer 1953- Problem 6

Source: Miklós Schweitzer 1953- Problem 6

August 3, 2015
Sequenceslimitcollege contests

Problem Statement

6. Let Hn(x)H_{n}(x) be the nth Hermite polynomial. Find lim⁡n→∞(y2n)nHn(ny) \lim_{n \to \infty } (\frac{y}{2n})^{n} H_{n}(\frac{n}{y}) For an arbitrary real y. (S.5)
Hn(x)=(−1)nex2dndxn(e−x2)H_n(x)=(-1)^n e^{x^2}\frac{d^n}{dx^n}\left(e^{{-x^2}}\right)
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