  The hypergeometric and Heun functions are classical special functions.
Transformation formulas between them are commonly induced by pull-back
transformations of their differential equations, with respect to some coverings
P1-to-P1. This gives expressions of Heun functions in terms of better
understood hypergeometric functions. This article presents the list of
hypergeometric-to-Heun pull-back transformations with a free continuous
parameter, and illustrates most of them by a Heun-to-hypergeometric reduction
formula. In total, 61 parametric transformations exist, of maximal degree 12.
