Towards a general theory of special functions
- 1 July 1972
- journal article
- Published by Association for Computing Machinery (ACM) in Communications of the ACM
- Vol. 15 (7) , 550-554
- https://doi.org/10.1145/361454.361466
Abstract
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).Keywords
This publication has 13 references indexed in Scilit:
- Algebraic simplificationCommunications of the ACM, 1971
- Automated algebraic manipulation in celestial mechanicsCommunications of the ACM, 1971
- Applications of symbol manipulation in theoretical physicsCommunications of the ACM, 1971
- Transcendental numbers and diophantine approximationsBulletin of the American Mathematical Society, 1971
- Construction of rational functions on a curveMathematical Proceedings of the Cambridge Philosophical Society, 1970
- On Canonical Forms and SimplificationJournal of the ACM, 1970
- The problem of integration in finite termsTransactions of the American Mathematical Society, 1969
- Solution of the identity problem for integral exponential functionsMathematical Logic Quarterly, 1969
- Algebraic Groups and Algebraic DependenceAmerican Journal of Mathematics, 1968
- Sur l'intégrabilité élémentaire de quelques classes d'expressionsCommentarii Mathematici Helvetici, 1945