Toward a General Theory of Special Functions A list of a number of natural developments for the field of algebraic manipulation is given. Then the prospects for a general theory of functions defined by ordinary differential equations are discussed. The claim is made that recent developments in mathematics indicate that it should be possible to algorithmically generate many properties of solutions to differential equations. Such a theory is preferable to a less general effort to make algebraic manipulation systems knowledgeable about the usual special functions (e.g. exponential, hypergeometric). CACM July, 1972 Moses, J. algebraic manipulation, special functions, algebraic simplification, symbolic integration, algebraic geometry, differential algebra 1.50 3.15 5.19 5.9 CA720705 JB January 30, 1978 3:07 PM 2164 4 2323 2170 4 2323 2323 4 2323 2323 4 2323 2323 4 2323 2719 4 2323 2167 5 2323 2164 5 2323 2170 5 2323 2323 5 2323 2323 5 2323 2323 5 2323