## Approximation of Gaussians by spherical Gauss-Laguerre basis in the weighted Hilbert space

### Abstract

This paper is devoted to the study of approximation of Gaussian functions by their partial Fourier sums of degree $N \in \mathbb{N}$ with respect to the spherical Gauss-Laguerre (SGL) basis in the weighted Hilbert space $L_2(\mathbb{R}^3, \omega_\lambda)$, where $\omega_\lambda(|\boldsymbol{x}|)=\exp({-|\boldsymbol{x}|^2/\lambda})$, $\lambda>0$. We investigate the behavior of the corresponding error of approximation with respect to the scale factor $\lambda$ and order of expansion $N$. As interim results we obtained formulas for the Fourier coefficients of Gaussians with respect to SGL basis in the space $L_2(\mathbb{R}^3, \omega_\lambda)$. Possible application of obtained results to the docking problem are described.

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### Key words

spherical harmonic, Laguerre polynomial, Gaussian, hypergeometric function, molecular docking

### AMS subject classifications

33C05, 33C45, 33C55, 42C10

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