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Dettweiler and Reiter formulated Euler's integral transformation for Fuchsian systems of differential equations and applied it to a definition of the middle convolution. In this paper, we formulate Euler's integral transformation for systems of linear differential equations with irregular singularities. We show by an example that the confluence of singularities is compatible with Euler's integral transformation.
Kouichi Takemura. "Euler's integral transformation for systems of linear differential equations with irregular singularities." Banach Center Publications 97.1 (2012): 141-152. <http://eudml.org/doc/281899>.
@article{KouichiTakemura2012, abstract = {Dettweiler and Reiter formulated Euler's integral transformation for Fuchsian systems of differential equations and applied it to a definition of the middle convolution. In this paper, we formulate Euler's integral transformation for systems of linear differential equations with irregular singularities. We show by an example that the confluence of singularities is compatible with Euler's integral transformation.}, author = {Kouichi Takemura}, journal = {Banach Center Publications}, keywords = {middle convolution; Euler's integral transformation; irregular singularity}, language = {eng}, number = {1}, pages = {141-152}, title = {Euler's integral transformation for systems of linear differential equations with irregular singularities}, url = {http://eudml.org/doc/281899}, volume = {97}, year = {2012}, }
TY - JOUR AU - Kouichi Takemura TI - Euler's integral transformation for systems of linear differential equations with irregular singularities JO - Banach Center Publications PY - 2012 VL - 97 IS - 1 SP - 141 EP - 152 AB - Dettweiler and Reiter formulated Euler's integral transformation for Fuchsian systems of differential equations and applied it to a definition of the middle convolution. In this paper, we formulate Euler's integral transformation for systems of linear differential equations with irregular singularities. We show by an example that the confluence of singularities is compatible with Euler's integral transformation. LA - eng KW - middle convolution; Euler's integral transformation; irregular singularity UR - http://eudml.org/doc/281899 ER -