.. index:: GramCharlier
This function implements the Gram-Charlier Series A expansion. It finds its main usage in fitting broad mass peaks in Y space within Neutron Compton Scattering experiments such as on the Vesuvio instrument at ISIS. As such the expansion includes only the even numbered Hermite polynomials, up to order 10, with the exception of the 3rd order term where it is useful to include a different amplitude factor.
The function definition is given by:
f(x) = A\frac{\exp(-z^2)}{\sqrt{2\pi\sigma^2}}(1 + \frac{C4}{(2^4(4/2)!)}H_4(z) +
\frac{C6}{(2^6(6/2)!)}H_6(z) + \frac{C8}{(2^8(8/2)!)}H_8(z) + \frac{C10}{(2^10(10/2)!)}H_{10}(z)) +
Afse\frac{\sigma\sqrt{2}}{12\sqrt{2\pi\sigma^2}}\exp(-z^2)H_3(z)
where z=\frac{(x-X_0)}{\sqrt{2\sigma^2}}, H_n(z) is the nth-order Hermite polynomial and the other parameters are defined in the properties table below.
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