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inlineconstexpr |
Computes the value of the 'physicists' Hermite polynomial of order n
at x
:
The physicists Hermite polynomials are a sequence of orthogonal polynomials relative to \(e^{-x^2}\) on the \([-\infty, +\infty]\) interval satisfying the following recurrence relation:
Defined in header
Parameters
Return value
The value of the 'physicists' hermite polynomial \( \displaystyle \mathbf{H}_n(x) = (-1)^n e^{x^2}\frac{d}{dx^n}e^{-x^2}\) is returned.
The expression successor(hermite)(n, x, Hn, Hnm1)
implements the three terms recurrence relation for the physicists Hermite polynomials, \(\displaystyle \mbox{H}_{n+1} = (2*x)\mbox{H}_{n}-2*n\mbox{H}_{n-1}\)
This function can be used to create a sequence of values evaluated at the same x
, and for rising n
.
Example