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• Fourier transform
  ...!\!\!\!\displaystyle (12) ~ ~ ~ A(x) ~=~ \sum_{n=0}^{\infty} ~c_n~ \mathrm{HermiteH}_{4n}\!(x)~ \exp(-x^2/2)\) where \(\mathrm{HermiteH}\) are the [[Hermit polynomial]]s
  11 KB (1,501 words) - 18:44, 30 July 2019
• CosFourier
  ...!\!\!\!\displaystyle (14) ~ ~ ~ f(x) ~=~ \sum_{n=0}^{\infty} ~c_n~ \mathrm{HermiteH}_{4n}\!(x)~ \exp(-x^2/2)\) where \(\mathrm{HermiteH}\) is the [[Hermite polynomial]]
  6 KB (915 words) - 18:26, 30 July 2019
• Amos
  \(H_n\!=\)[[HermiteH]]\(_n\) is the \(nth\) [[Hermite polynomial]], [[HermiteH]],
  6 KB (883 words) - 18:44, 30 July 2019
• Amplitude of oscillator function
  where \(\psi_n(z)=\frac{1}{\sqrt{N_n}}\)[[HermiteH]]\(_n(z)\, \exp(-z^2/2)\) is [[oscillator function]], here, [[HermiteH]]\(_n\) denotes the \(n\)th [[Hermite polynomial]] and \(N_n\) is its norm.
  6 KB (770 words) - 18:44, 30 July 2019
• Hermite Gauss mode
  F[x_] = ((w+I z)^(-1/2-m/2) HermiteH[m,x/(Sqrt[2] Sqrt[w+I z])]) Exp[-x^2/(2(w+I z))] f[x_]=E^(-x^2/(2(o+I z)) - (I/2) (1+2m) ArcTan[z/o]) HermiteH[m,x/Sqrt[o+z^2/o]])/(1+z^2/o^2)^(1/4)
  8 KB (1,216 words) - 18:43, 30 July 2019
• Hermite polynomial
  The \(m\)th Hermite polynomial is denoted with \(H_m(x)=\mathrm{HermiteH}[m,x]\). \(\displaystyle h_n(z)= \frac{1}{\sqrt{N_n}} \mathrm{HermiteH}[n,x]=\frac{H_n(x)}{\sqrt{N_n}}\)
  4 KB (628 words) - 18:47, 30 July 2019
• Oscillator function
  \(H_n(x)=\mathrm{HermiteH}[n,x]\) \(H_n=H_n(0)=\mathrm{HermiteH}[n,0]\).
  6 KB (846 words) - 18:47, 30 July 2019
• SinFT
  \(F(x)=\,\)[[OscillatorFunction]]\(_{2n+1}(x)=\,\)[[HermiteH]]\(_{2n+1}(x)\,\exp(-x^2/2)\)
  5 KB (807 words) - 18:44, 30 July 2019