11-50 S. Malek, C. Stenger

On complex singularity analysis of holomorphic solutions of linear partial differential equations (489K, postscript) Mar 25, 11

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Abstract. We construct formal series solutions of linear partial differential equations as linear combinations of powers of solutions of first order nonlinear differential equations, following the classical tanh method. We give sufficient conditions under which the constructed formal series define holomorphic functions on some products of punctured discs of the complex plane. Moreover, we study the rate of growth of these solutions near their singular points

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