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BRAAKSMA, B.L.J., Laplace integrals, factorial series and singular differential equations, Proc. Bicentennial congress of the Wiskundig Genootschap, Amsterdam 1978.
BRAAKSMA, B.L.J. & W.A. Harris, Jr., Laplace integrals and factorial series in singular differential systems. To appear in Applicable Mathematics.
DOETSCH, G., Handbuch der Laplace Transformation, Band II. Birkhäuser Verlag, Basel, 1955.
ERDELYI, A., The integral equations of asymptotic theory, in Asymptotic Solutions of Differential Equations and their Applications, edited by C.H. Wilcox, John Wiley, New York, 1964, 211–229.
HARRIS, Jr., W.A. & Y. SIBUYA, Note on linear difference equations, Bull. Amer. Math. Soc., 70 (1964) 123–127.
HARRIS, Jr. W.A. & Y. SIBUYA, Asymptotic solutions of systems of nonlinear difference equations, Arch. Rat. Mech. Anal., 15 (1964) 377–395.
HARRIS, Jr., W.A. & Y. SIBUYA, On asymptotic solutions of systems of non-linear difference equations, J.reine angew.Math., 222 (1966) 120–135.
HORN, J., Integration linearer Differentialgleichungen durch Laplacesche Integrale und Fakultätenreihen. Jahresber. Deutsch. Math.Ver., 24 (1915) 309–329; 25 (1917) 74–83.
HORN, J., Laplacesche Integrale als Lösungen von Funktionalgleichungen, J. reine angew. Math., 146 (1916) 95–115.
HORN, J., Verallgemeinerte Laplacesche Integrale als Lösungen linearer und nichtlinearer Differentialgleichungen. Hahresber. Deutsch. Math. Ver., 25 (1917) 301–325.
HORN, J., Über eine nichtlineare Differenzengleichung, Jahresber. Deutsch. Math. Ver., 26 (1918) 230–251.
HORN, J., Laplacesche Integrale, Binomialkoeffizientenreihen und Gamma-quotientenreihen in der Theorie der linearen Differentialgleichungen. Math. Zeitschr., 21 (1924) 85–95.
HUKUHARA, M., Intégration formelle d'un système des équations différentielles non linéaires dans le voisinage d'un point singulier. Ann. Mat. Pura Appl., (4) 19 (1940) 35–44.
IWANO, M., Analytic expressions for bounded solutions of non-linear ordinary differential equations with an irregular type singular point. Ann. Mat. Pura Appl., (4) 82 (1969) 189–256.
IWANO, M., Analytic integration of a system on nonlinear ordinary differential equations with an irregular type singularity. Ann. Mat. Pura Appl., (4) 94 (1972) 109–160.
MALMQUIST, J., Sur l'étude analytique des solutions d'un système d'équations différentielles dans le voisinage d'un point singulier d'indétermination, II. Acta Math., 74 (1941) 1–64.
TRJITZINSKY, W.J., Laplace integrals and factorial series in the theory of linear differential and difference equations, Trans. Amer. Math. Soc., 37 (1934) 80–146.
TURRITTIN, H.L., Convergent solutions of ordinary linear homogeneous differential equations in the neighbourhood of an irregular singular point. Acta Math., 93 (1955) 27–66.
TURRITTIN, H.L., The formal theory of systems of irregular homogeneous linear difference and differential equations, Bol.Soc.Math. Mexicana (1960) 255–264.
TURRITTIN, H.L., A canonical form for a system of linear difference equations, Ann. Mat. Pura Appl., 58 (1962) 335–357.
TURRITTIN, H.L., Reducing the rank of ordinary differential equations. Duke Math. J., 30 (1963) 271–274.
TURRITTIN, H.L., Solvable related equations pertaining to turning point problems, in Asymptotic Solutions of Differential Equations and their Applications. Edited by C.H. Wilcox, John Wiley, New York, 1964, 27–52.
WALTER, W., Differential-and Integral Inequalities. Springer Verlag, Berlin, 1970.
WASOW, W., Asymptotic expansions for ordinary differential equations. Interscience Publishers, New York, 1965.
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Braaksma, B.L.J. (1980). Laplace integrals in singular differential and difference equations. In: Everitt, W.N. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0091373
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