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Formula manipulations solving linear ordinary differential equations. II. (English) Zbl 0339.68037


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
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[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
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[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.
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[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
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[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
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