Hermite Interpolation - MATH 375 Numerical Analysis The Hermite polynomials H(x) agree with f(x) and the derivatives of the Hermite polynomials H′(x) agree with f′(x) The degree of the Hermite polynomial is 2n + 1 since 2n + 2 conditions must be met (n + 1 points and n + 1 derivatives)
Hermite polynomials - Encyclopedia of Mathematics One possible way to prove the Plancherel formula for the Fourier transform is by use of Hermite polynomials, cf [a4] Hermite polynomials occur in solutions of the heat and Schrödinger equations and in the so-called heat polynomials, cf [a1]
Hermite and Laguerre Polynomials - Charleston Hermite polynomials are solutions of the simple harmonic oscillator of quan-tum mechanics Their properties directly follow from writing their ODE as a product of creation and annihilation operators and the Sturm–Liouville theory of their ODE