Watanabe, Shunro Formula manipulations solving linear ordinary differential equations. II. (English) Zbl 0339.68037 Publ. Res. Inst. Math. Sci., Kyoto Univ. 11, 297-337 (1976). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 Document MSC: 68W30 Symbolic computation and algebraic computation 65Lxx Numerical methods for ordinary differential equations 34A05 Explicit solutions, first integrals of ordinary differential equations 34A30 Linear ordinary differential equations and systems 65J99 Numerical analysis in abstract spaces Software:REDUCE; MACSYMA; ALGOL 68; ALGOL 60 PDFBibTeX XMLCite \textit{S. Watanabe}, Publ. Res. Inst. Math. Sci. 11, 297--337 (1976; Zbl 0339.68037) Full Text: DOI References: [1] Hukuhara, M., Integration methods of linear ordinary differential equations II (linear equations), Iwanami 1941 (in Japanese). [2] Hukuhara, M., On Fuchsian equations which are changeable to each other by linear transformations, Jour, of Tsuda College, 2 (1970), 1-12 (in Japanese). [3] Hukuhara, M. and Ohashi, S., On the determination of Types of Riemann’s .P-funetion which can be expressed by elementary functions, Sugaku, (1949), 227-230 (in Japanese). [4] Hukuhara, M. and Ohashi, S., On Riemann’s P-function which is expressed by elementary functions, Sugaku, (1952), 27-29 (in Japanese). [5] Kimura, T., On Riemann’s Equations which are Solvable by Quadratures, Funkdal. Ekvac., 12 (1969), 269-281. · Zbl 0198.11601 [6] Kimura, T., On Fuchsian Differential Equations reducible to Hypergeometric Equations by Linear Transformations, Funkdal. Ekvaci., 13 (1970), 213-232. · Zbl 0255.34005 [7] Schwarz, H. A., Uber diejenigen Falle, in welchen die Gaussische hypergeomet- rische Reihe eine algebraische Function ihres vierten Elements darstellt, /. Reine Angew. Math., (1872), 292-335. · JFM 05.0146.03 [8] Cayley, A., On the Schwarzian Derivative, and the Polyhedral Functions. Trans of the Cambridge Phil. Soc., III. Part I (1881), 5-68, Oeuvre 745. [9] Picard, C, Traite d’analyse, 3, chapitre II-III. 1928. [10] Goursat, E., Lemons sur les Series Hypergeometriques et sur quelque fonctions s’y rattachent, I. Proprietes Generates de L’equation D’Euler et DE GAUSS II. Integrates Algebriques probleme D’inversion. · Zbl 0014.06202 [11] Kamke, E., Differ entialgleichungen, Losungsmethoden und Losungen, 1948, New York, Chelsea. · Zbl 0041.05402 [12] Murphy, G., Ordinary Differential Equations and their Solutions. Van Nostrand, Reinhold, 1960. · Zbl 0095.06405 [13] McCarthy, J., et al., LISP 1.5 Programmer’s Manual. The M. I. T. Press. 2nd edition 1969. [14] Naur, P., et al., Revised Report on the Algorithmic Language ALGOL-60, Comm. ACM., 6 (Jan. 1963), 1-17. · Zbl 0109.35105 [15] Iwamura, T., Kakehi, K., Sakuma, K., Simauti, T., Wada, E. and Yoneda, N., ALGOL-N, Comment. Math. Univ. St. PaulL, XXI-1 (1972). [16] van Wijngaarden (editor) et al., Report on the algorithmic language ALGOL 68, The Mathematisch Centrum, Amsterdam, MR101, Oct. 1969. [17] Martin, W., Fateman, R., Moses, J. and Wang, P., The MACSYMA, Papers 1970 Second Symposium on Symbolic and Algebraic Manipulation held March 23-25, 1971 in Los Angels. [18] Bobrow, J. (editor), Symbol Manipulation Languages and Techniques, North- Holland, 1968. · Zbl 0179.30607 [19] Hearn, A. C., REDUCE 2, User’s Manual, University of Utah, 1973. [20] Watanabe, S., Formula Manipulations Solving Linear Ordinary Differential Equations I. Publ, RIMS, Kyoto Univ., 6 (1970), 71-111, · Zbl 0242.68018 · doi:10.2977/prims/1195194188 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.