  The established technique of eliminating upper or lower parameters in a
general hypergeometric series is profitably exploited to create pathways among
confluent hypergeometric functions, binomial functions, Bessel functions, and
exponential series. One such pathway, from the mathematical statistics point of
view, results in distributions which naturally emerge within nonextensive
statistical mechanics and Beck-Cohen superstatistics, as pursued in
generalizations of Boltzmann-Gibbs statistics.
