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Using entropic inequalities for Shannon entropies new inequalities for someclassical polynomials are obtained. To this end, photon distribution functionsfor one-, two- and multi-mode squeezed states in terms of Hermite, Laguerre,Legendre polynomials and Gauss' hypergeometric functions are used. Thedependence between the violation of the quadrature uncertainty relation, thesign and the existence of the distribution function of such states isconsidered.

Photon distributions and information nonnegativity versus quadrature uncertainty relation