Middle Convolution and Heun’s Equation
نویسندگان
چکیده
The parameter q is called an accessory parameter. Although the local monodromy (local exponent) is independent of q, the global monodromy (e.g. the monodromy on the cycle enclosing two singularities) depends on q. Some properties of Heun’s equation are written in the books [21, 23], but an important feature related with the theory of finite-gap potential for the case γ, δ, ǫ, α−β ∈ Z+ 12 (see [6, 24, 25, 26, 27, 28, 29, 31] etc.), which leads to an algorithm to calculate the global monodromy explicitly for all q, is not written in these books. The sixth Painlevé equation is a non-linear ordinary differential equation written as
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