Abstract
In this chapter, we consider a continuous counterpart of Gosper’s algorithm. The appropriate question is to find a hyperexponential term antiderivative G(x) of a given f(x) whenever one exists.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
For details see, e.g., [DST88], Appendix.
- 2.
This result may depend on the version of Maple you use.
References
Almkvist, G., Zeilberger, D.: The method of differentiating under the integral sign. J. Symbolic Comput. 10, 571–591 (1990)
Bronstein, M.: Integration and differential equations in computer algebra. Programmirovanie 18(5), 26–44 (1992)
Bronstein, M.: Introduction to Symbolic Integration. Algorithms and Computation in Mathematics, vol. 1. Springer, Berlin (1996)
Davenport, J.H., Siret, Y., Tournier, E.: Computer Algebra: Systems and Algorithms for Algebraic Computation. Academic Press, London (1988)
Geddes, Ko, Czapor, S.R., Labahn, G.: Algorithms for Computer Algebra. Kluwer Academic Publishers, Boston, Dordrecht, London (1992)
Risch, R.: The problem of integration in finite terms. Trans. Amer. Math. Soc. 139, 167–189 (1969)
Risch, R.: The solution of the problem of integration in finite terms. Bull. Amer. Math. Soc. 76, 605–608 (1970)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer-Verlag London
About this chapter
Cite this chapter
Koepf, W. (2014). Hyperexponential Antiderivatives. In: Hypergeometric Summation. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-6464-7_11
Download citation
DOI: https://doi.org/10.1007/978-1-4471-6464-7_11
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-4471-6463-0
Online ISBN: 978-1-4471-6464-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)