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 discrete
Student-type distributions with odd degrees of freedom.
Keywords: Fourier series; discrete Student distribution; Cauchy-Cacoullos
family.Comment: Dedicated to Professor Theo Cacoullos (13 pages, 1 Figure