Geodesic
The probability properties of bilinear expansions in Hermite polynomiels
Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 3, pp. 520-531

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The present paper contains an investigation of the probability meaning of formulas (1) and (4). According to the basic theorem 2 for sum (1) to be non negative it is nesessary and sufficient that the sequence of coefficients $\{c_k\}$ be the sequence of moments of some probability distribution in finite interval $[-1,1]$. Some examples of densities comprised in the normal class in the sence of Fré'chet [7] are given here. 
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     author = {O. V. Sarmanov and Z. N. Bratoeva},
     title = {The probability properties of bilinear expansions in {Hermite} polynomiels},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {520--531},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {1967},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1967_12_3_a9/}
}
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O. V. Sarmanov; Z. N. Bratoeva. The probability properties of bilinear expansions in Hermite polynomiels. Teoriâ veroâtnostej i ee primeneniâ, Tome 12 (1967) no. 3, pp. 520-531. http://geodesic.mathdoc.fr/item/TVP_1967_12_3_a9/