Kouichi Takemura, “Middle Convolution and Heun's Equation”, SIGMA, 2009, Volume 5,040, 22 pp.

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Middle Convolution and Heun's Equation

Kouichi Takemura

Department of Mathematical Sciences, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama 236-0027, Japan

Abstract: Heun's equation naturally appears as special cases of Fuchsian system of differential equations of rank two with four singularities by introducing the space of initial conditions of the sixth Painlevé equation. Middle convolutions of the Fuchsian system are related with an integral transformation of Heun's equation.

Keywords: Heun's equation; the space of initial conditions; the sixth Painlevé equation; middle convolution.

MSC: 34M35; 33E10; 34M55

Received: November 26, 2008; in final form March 25, 2009; Published online April 3, 2009

Language: English

DOI: 10.3842/SIGMA.2009.040