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The Pólya–Szegő inequality is a result in the field of mathematics, particularly in the area of functional analysis and inequalities. It provides a comparison of certain integral expressions that involve non-negative functions, and it is often used in the context of orthogonal polynomials and convex functions. More specifically, the Pólya–Szegő inequality deals with the integrals of non-negative functions defined on the interval \([0, 1]\).