A Structure Theorem for Exponential and Primitive Functions
Michael Rothstein, Bob F. Caviness · SIAM Journal on Computing · 1979
In this paper a new theorem is proved that generalizes a result of Risch. The new theorem gives all the possible algebraic relationships among functions that can be built up from the rational functions by algebraic operations, by taking exponentials, and by integration. The functions so generated are called exponential and primitive functions. From the theorem an algorithm for determining algebraic dependence among a given set of exponential and primitive functions is derived. The algorithm is then applied to a problem in computer algebra.