# Evaluation of product of Hermitian functions
**URL:** https://discourse.julialang.org/t/evaluation-of-product-of-hermitian-functions/42316
**Category:** Numerics
**Tags:** polynomials
**Created:** [June 30, 2020, 6:07pm UTC](https://discourse.julialang.org/t/evaluation-of-product-of-hermitian-functions/42316 "2020-06-30T18:07:00Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@mleprovost](https://discourse.julialang.org/u/mleprovost)
#### Post date: [June 30, 2020, 6:07pm UTC](https://discourse.julialang.org/t/evaluation-of-product-of-hermitian-functions/42316/1 "2020-06-30T18:07:00Z")
Hello,
I am working on expansion of a multivariate function f : R^k \xrightarrow{} R onto a basis of product of univariates Hermite functions:
f(x\_1, x\_2, \ldots, x\_k) = \sum\_{\boldsymbol{\alpha}} c\_{\boldsymbol{\alpha}} \psi\_{\boldsymbol{\alpha}}(x\_1, x\_2, \ldots, x\_k) ,
where \boldsymbol{\alpha} = (\alpha\_1, \ldots, \alpha\_k) is a multi-index and \psi\_{\boldsymbol{\alpha}}(x\_1, x\_2, \ldots, x\_k) = \prod\_{j=1}^k \psi\_{\alpha\_j}(x\_j) and the \psi\_{\alpha\_j} are Hermite functions given by \psi\_{\alpha\_j}(x) = P\_{\alpha\_j}(x)\exp(-x^2/4).
Is there a Julia package that implements multivariate Hermite polynomials? k will usually be of order 50 and the degree of each polynomial will usually be less than 7-8, and I expect sparse decomposition so some multi-index coefficients \alpha\_j will be zero.
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### Author:  [@platawiec](https://discourse.julialang.org/u/platawiec)
#### Post date: [June 30, 2020, 8:03pm UTC](https://discourse.julialang.org/t/evaluation-of-product-of-hermitian-functions/42316/2 "2020-06-30T20:03:35Z")
You can use an expansion over a `Hermite` space via [https://github.com/JuliaApproximation/ApproxFun.jl](https://github.com/JuliaApproximation/ApproxFun.jl)
See the following documentation: [Spaces · ApproxFun.jl](https://juliaapproximation.github.io/ApproxFun.jl/stable/usage/spaces/) and [Library · ApproxFun.jl](https://juliaapproximation.github.io/ApproxFun.jl/stable/library/#ApproxFunOrthogonalPolynomials.Hermite)