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A new family of integer-valued Cauchy-type distributions is introduced, the{\it Cauchy-Cacoullos family}. The characteristic function is evaluated,showing some interesting distributional properties, similar to the ordinary(continuous) Cauchy scale family. The results are extendable to discreteStudent-type distributions with odd degrees of freedom.  Keywords: Fourier series; discrete Student distribution; Cauchy-Cacoullosfamily.

The characteristic function of the discrete Cauchy distribution (In Memory of T. Cacoullos)