Hermite Polynomial Calculator

H_n(x) = (-1)^n e^{x²} d^n/dx^n e^{-x²}

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n (degree)

Physicist H_5

-8

Probabilist He_5

Sequence at x=1

n=0H=1He=1

n=1H=2He=1

n=2H=2He=0

n=3H=-4He=-2

n=4H=-20He=-2

n=5H=-8He=6

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About Hermite Polynomial Calculator

A Hermite polynomial calculator computing (physicist's) H_n(x) via recurrence H_{n+1}=2xH_n−2nH_{n-1}. H_0=1, H_1=2x, H_2=4x²−2, H_3=8x³−12x. Quantum harmonic oscillator wavefunctions ψ_n ∝ H_n(x)e^{-x²/2}. Client-side.

Hermite Polynomial Calculator Features

H_n(x) value
Probabilist He_n
Coefficients
QHO connection
Sequence

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