  Euler's transformation formula for the Gauss hypergeometric function 2F1 is
extended to hypergeometric functions of higher order. Unusually, the
generalized transformation constrains the hypergeometric function parameters
algebraically but not linearly. Its consequences for hypergeometric summation
are explored. It has as corollary a summation formula of Slater. From this
formula new one-term evaluations of 2F1(-1) and 3F2(1) are derived, by applying
transformations in the Thomae group. Their parameters are also constrained
nonlinearly. Several new one-term evaluations of 2F1(-1) with linearly
constrained parameters are derived as well.
