Geodesic
A generalization of the Schwarz--Christoffel formula
Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 4, pp. 109-117.

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We obtain a formula for mapping the upper half-plane conformally onto a polygonal region, generalizing the Schwarz–Christoffel formula to the case of a countable set of vertices. We indicate a connection of the construction of this mapping to the solution of the Hilbert boundary value problem with a countable set of discontinuity points of the coefficients and polynomial singularity of the index.
Keywords: the Schwarz–Christoffel formula, boundary conditions, index of the problem. 
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R. B. Salimov; P. L. Shabalin. A generalization of the Schwarz--Christoffel formula. Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 4, pp. 109-117. http://geodesic.mathdoc.fr/item/SJIM_2010_13_4_a9/

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