Published: 1980 Received: December 13, 1978Available on J-STAGE: October 20, 2006Accepted: -
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Date of correction: October 20, 2006Reason for correction: -Correction: CITATIONDetails: Right : [1] C. Chevalley, Introduction to the theory of algebraic functions of one variable, Math. Surveys 6, Amer. Math. Soc., 1951. [2] E. R. Kolchin, Existence theorems connected with the Picard-Vessiot theory of homogeneous linear ordinary differential equations, Bull. Amer. Math. Soc., 54 (1948), 927-932. [3] J. Liouville, Mémoire sur la classification des transcendantes, et sur l'impossibilité d'éxprimer les racines des certaines des équations en fonction finie explicate des coefficients, J. Math. Pures Appl., 2 (1837), 56-104. [4] D. Mordukhai-Boltovskoi, Sur la résolution des équations différentielles de premier ordre en forme finie, Rend. Circ. Mat. Palermo, 61 (1937), 49-72. [5] S. Otsubo, Order of liouvillian elements satisfying an algebraic differential equation of the first order, Osaka J. Math., 16 (1979), 667-673. [6] J. F. Ritt, Integration in finite terms, Columbia Univ. Press, New York, 1948. [7] M. Rosenlicht and M. F. Singer, On elementary, generalized elementary, and liouvillian extension field,“Contributions to Algebra”, Academic Press, New York, 1977, 329-342. [8] M. F. Singer, Elementary solutions of differential equations, Pacific J. Math., 59 (1975), 535-547. [9] G. N. Watson, A treaties on the theory of Bessel functions, Cambridge Univ. Press, London, 1922.
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