Rational Landen transformations on ℝ

Mathematics of Computation

Volumn 76, Issue 260, 2007, Pages 2023-2043

  Manna, Dante ^a,b   Moll, Victor H ^a  

^a Tulane University   (United States)

^b DALHOUSIE UNIVERSITY   (Canada)

Author keywords

Integrals; Transformations

Indexed keywords

EID: 38849084530     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-07-01954-0     Document Type: Article

References (22)

1. G. Andrews, R. Askey, and R. Roy, Special Functions, Encyclopedia of Mathematics and its Applications, vol. 71, Cambridge University Press, New York, 1999. MR1688958 (2000g:33001)
2. M. Artin, Algebra, Prentice Hall, Englewood Cliffs, New Jersey, 1991. MR1129886 (92g:00001)
3. G. Boros, O. Espinosa, and V. Moll, On some families of integrals solvable in terms of polygamma and negapolygamma functions, Integrals Transforms and Special Functions 14 (2003), 187-203. MR1982825 (2004f:33004)
4. G. Boros and V. Moll, A rational Landen transformation. The case of degree 6, Contemporay Mathematics. Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis (Knopp G., Mendoza E.T., Quinto E. L., Grinberg S., Berhanu M., eds.), vol. 251, American Mathematical Society, 2000, pp. 83-89. MR1771260 (2001h:33029)
5. _, Landen transformation and the integration of rational functions, Math. Comp. 71 (2001), 649-668. MR1885619 (2004c:33044)
6. J. M. Borwein and P. B. Borwein, Pi and the AGM. A study in analytic number theory and computational complexity, 1st ed., Wiley, New York, 1987. MR877728 (89a:11134)
7. M. Bronstein, Symbolic integration. I. Transcendental functions, Algorithms and Computation in Mathematics, vol. 1, Springer-Verlag, 1997. MR1430096 (98a:68104)
8. M. Chamberland and V. Moll, Dynamics of the degree six Landen transformation, Discrete and Dynamical Systems 15 (2006), no. 3, 905-919. MR2220755 (2006m:39012)
9. K. F. Gauss, Arithmetisch Geometrisches Mittel, Werke 3 (1799), 361-432.
10. _, Disquisitiones generales circa seriem infinitam, Werke 3 (1812), 123-162.
11. K. Geddes, S. R. Czapor, and G. Labahn, Algorithms for computer algebra, Kluwer, Dordrecht, The Netherlands, 1992. MR1256483 (96a:68049)
12. I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, 6th ed., Edited by A. Jeffrey and D. Zwillinger. Academic Press, New York, 2000. MR1773820 (2001c:00002)
13. eme serie) 11 (1872), 145-148.
14. E. Horowitz, Algorithms for partial fraction decomposition and rational function integration, Proc. of SYMSAM'71, ACM Press (1971), 441-457.
15. J. Hubbard and V. Moll, A geometric view of rational Landen transformation, Bull. London Math. Soc. 35 (2003), 293-301. MR1960939 (2003k:33028)
16. D. Lazard and R. Rioboo, Integration of rational functions: rational computation of the logarithmic part, Journal of Symbolic Computation 9 (1990), 113-116. MR1056840 (91h:68091)
17. D. Manna and V. Moll, A simple example of a new class of Landen transformations, American Mathematical Monthly 114 (2007), 232-241. MR2290287
18. H. McKean and V. Moll, Elliptic Curves: Function Theory, Geometry, Arithmetic, Cambridge University Press, New York, 1997. MR1471703 (98g:14032)
19. M. W. Ostrogradsky, De l'integration des fractions rationelles, Bulletin de la Classe Physico-Mathematiques de l'Academie Imperiale des Sciences de St. Petersbourgh IV (1845), 145-167, 286-300.
20. J. F. Ritt, Permutable rational functions, Trans. Amer. Math. Soc. 25 (1923), 399-448. MR1501252
21. M. Rothstein, A new algorithm for the integration of exponential and logarithmic functions, Proc. of the 1977 MACSYMA Users Conference, NASA Pub., CP-2012 (1977), 263-274.
22. B. M. Trager, Algebraic factoring and rational function integration, Proc. SYMSAC (1976), 219-226.