×

Symbolic computation of parameter integrals. (English) Zbl 1360.68952

Rosenkranz, Markus (ed.), Proceedings of the 41st international symposium on symbolic and algebraic computation, ISSAC 2016, Waterloo, Canada, July 20–22, 2016. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-4380-0). 13-15 (2016).

MSC:

68W30 Symbolic computation and algebraic computation
12H05 Differential algebra
Full Text: DOI

References:

[1] G. E. T. Almkvist and D. Zeilberger. The method of differentiating under the integral sign. J. Symb. Comput., 10:571-591, 1990. 10.1016/S0747-7171(08)80159-9 · Zbl 0717.33004
[2] M. Apagodu and D. Zeilberger. Multi-variable Zeilberger and Almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory. Adv. Appl. Math., 37:139-152, 2006. 10.1016/j.aam.2005.09.003 · Zbl 1108.05010
[3] S. T. Boettner, Mixed Transcendental and Algebraic Extensions for the Risch-Norman Algorithm, PhD Thesis, Tulane Univ., New Orleans, USA, 2010.
[4] A. Bostan, S. Chen, F. Chyzak, Z. Li, and G. Xin. Hermite Reduction and Creative Telescoping for Hyperexponential Functions. In Proc. ISSAC 2013, pp. 77-84, 2013. 10.1145/2465506.2465946 · Zbl 1360.68918
[5] M. Bronstein. Integration of Elementary Functions. J. Symb. Comput., 9:117-173, 1990. 10.1016/S0747-7171(08)80027-2 · Zbl 0718.12006
[6] M. Bronstein. Symbolic Integration I – Transcendental Functions. 2nd ed., Springer, 2005. · Zbl 1059.12002
[7] S. Chen, M. Kauers, and C. Koutschan. A Generalized Apagodu-Zeilberger Algorithm. In Proc. ISSAC 2014, pp. 107-114, 2014. 10.1145/2608628.2608641 · Zbl 1325.68270
[8] S. Chen, M. Kauers, and M. F. Singer. Telescopers for Rational and Algebraic Functions via Residues. In Proc. ISSAC 2012, pp. 130-137, 2012. 10.1145/2442829.2442851 · Zbl 1323.68592
[9] G. W. Cherry. Integration in Finite Terms with Special Functions: the Error Function. J. Symb. Comput., 1:283-302, 1985. 10.1016/S0747-7171(85)80037-7 · Zbl 0586.68030
[10] G. W. Cherry. Integration in finite terms with special functions: the logarithmic integral. SIAM J. Comput., 15:1-21, 1986. 10.1137/0215001 · Zbl 0612.12019
[11] F. Chyzak. An extension of Zeilberger’s fast algorithm to general holonomic functions. Discrete Math., 217:115-134, 2000. 10.1016/S0012-365X(99)00259-9 · Zbl 0968.33011
[12] F. Chyzak. The ABC of Creative Telescoping – Algorithms, Bounds, Complexity. Habilitation à diriger des recherches (HDR), Univ. Paris-Sud 11, France, 2014. http://specfun.inria.fr/chyzak/Chyzak-2014-ABC.pdf
[13] F. Chyzak, M. Kauers, and B. Salvy. A Non-Holonomic Systems Approach to Special Function Identities. In Proc. ISSAC 2009, pp. 111-118, 2009. 10.1145/1576702.1576720 · Zbl 1237.33001
[14] F. Chyzak and B. Salvy. Non-commutative elimination in Ore algebras proves multivariate identities. J. Symb. Comput., 26:187-227, 1998. 10.1006/jsco.1998.0207 · Zbl 0944.05006
[15] K. O. Geddes, M. L. Glasser, R. A. Moore, T. C. Scott. Evaluation of Classes of Definite Integrals Involving Elementary Functions via Differentiation of Special Functions. Appl. Alg. Eng. Comm. Comp., 1:149-165, 1990. · Zbl 0726.33015
[16] C. Koutschan. Creative Telescoping for Holonomic Functions. In Computer Algebra in Quantum Field Theory, pp. 171-194, Springer, 2013. · Zbl 1308.81102
[17] A. C. Norman and P. M. A. Moore. Implementing the new Risch Integration algorithm. In Proc. 4th International Colloquium on Advanced Computing Methods in Theoretical Physics, pp. 99-110, 1977.
[18] A. van der Poorten. A Proof that Euler Missed... Apéry’s Proof of the Irrationality of ζ(3)\( -- An Informal Report. Math. Intelligencer, 1:195-203, 1979\) · Zbl 0409.10028
[19] C. G. Raab. Definite Integration in Differential Fields. PhD Thesis, Johannes Kepler Univ. Linz, Austria, 2012. http://www.risc.jku.at/publications/download/risc_4583/PhD_CGR.pdf
[20] R. H. Risch. The problem of integration in finite terms. Trans. Amer. Math. Soc., 139:167-189, 1969. · Zbl 0184.06702
[21] M. Rosenlicht. Liouville’s theorem on functions with elementary integrals. Pacific J. Math., 24:153-161, 1968. · Zbl 0155.36702
[22] C. Schneider. A difference ring theory for symbolic summation. J. Symb. Comput., 72:82-127, 2016. 10.1016/j.jsc.2015.02.002 · Zbl 1328.12015
[23] M. F. Singer, B. D. Saunders, and B. F. Caviness. An Extension of Liouville’s Theorem on Integration in Finite Terms. SIAM J. Comput., 14:966-990, 1985. · Zbl 0575.12021
[24] N. Takayama. An algorithm of constructing the integral of a module – an infinite dimensional analog of Gröbner basis. In Proc. ISSAC’90, pp. 206-211, 1990. 10.1145/96877.96929
[25] B. M. Trager. Integration of simple radical extensions. In Proc. EUROSAM’79, pp. 408-414, 1979. · Zbl 0411.12020
[26] B. M. Trager. Integration of algebraic functions. PhD Thesis, MIT, USA, 1984.
[27] D. Zeilberger. A holonomic systems approach to special functions identities. J. Comp. Appl. Math., 32:321-368, 1990. 10.1016/0377-0427(90)90042-X · Zbl 0738.33001
[28] D. Zeilberger. The Method of Creative Telescoping. J. Symb. Comput., 11:195-204, 1991. 10.1016/S0747-7171(08)80044-2 · Zbl 0738.33002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.