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For each given p > 1, we minimize the integral /_111 — /(a:)| da: over all entire functions / belonging to the Laguerre-Polya class having x = — 1 and x = 1 as consecutive zeros. The extremal function turns out to be of the form c(l — x) where c depends on p. The case p = 1 of the problem was considered earlier by J. G. Clunie.

Approximation by entire functions belonging to the Laguerre–Polya class