Functions of Several Complex Variables and Their Singularities

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Removable singularities are not poles.

For example, the function has the following singularities: poles at , and a nonisolated singularity at 0. Knopp, K. New York: Dover, pp.


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Functions of Several Complex Variables and Their Singularities

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  7. Collection of teaching and learning tools built by Wolfram education experts: dynamic textbook, lesson plans, widgets, interactive Demonstrations, and more. Solving this system we represent a solution to the Horn system in the form of an iterated Puiseux series. We give an explicit formula for the dimension of the space of analytic solutions to the Horn system at a generic point under some assumptions on its parameters.

    The proof is based on the study of the module over the Weyl algebra of linear differential operators with polynomial coefficients associated with the Horn system. Combining this formula with the theorem which allows one to represent a solution to the Horn system in the form of an iterated Puiseux series, we obtain a basis in the space of analytic solutions to this system of equations.

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    Another object of study in the thesis is the singular set of a nonconuent hypergeometric function in several variables. Typically such a function is a multi-valued analytic function with singularities along an algebraic hypersurface. We give a description of such hypersurfaces in terms of the Newton polytopes of their defining polynomials.

    SINGULARITIES OF SMOOTH MAPPINGS

    In particular we obtain a geometric description of the zero set of the discriminant of a general algebraic equation. In the case of two variables one can say much more about singularities of nonconuent hypergeometric functions. The most local data of importance, major of sinking techniques from Tutorials step and producing the matrix within non-ionizing corals.

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