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In his beautiful monograph Mark Kac began with a
proof of Vieta's formula using the Rademacher functions and their
independence property, and in the first chapter, a generalization of Vieta's formula was
suggested as an exercise. In this
paper we provide a proof following Kac's idea of using the independence property of the Rademacher
functions. To the best of our knowledge, this generalization has only been
achieved by Kent E. Morrison using the Fourier transform and delta
distributions
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