Towards a general theory of special functions
Communications of the ACM
Symbolic integration: the stormy decade
Communications of the ACM
An extension of Liouville's theorem
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Integration of simple radical extensions
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Integration -- the dust settles? (invited)
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Completing the L-th power in Z[x]
ACM SIGSAM Bulletin
Computer Algebra: Past and Future
Journal of Symbolic Computation
Integration of Liouvillian functions with special functions
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
Indefinite integration with validation
ACM Transactions on Mathematical Software (TOMS)
Formal solutions of differential equations
Journal of Symbolic Computation
Computer algebra handbook
What Might "Understand a Function" Mean?
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
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A decision procedure for integrating a class of transcendental elementary functions in terms of elementary functions and error functions is described. The procedure consists of three mutually exclusive cases. In the first two cases a generalised procedure for completing squares is used to limit the error functions which can appear in the integral to a finite number. This reduces the problem to the solution of a differential equation and we use a result of Risch (1969) to solve it. The third case can be reduced to the determination of what we have termed E-decompositions. The result presented here is the key procedure to a more general algorithm which is described fully in Cherry (1983).