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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     author = {R. B. Salimov and P. L. Shabalin},
     title = {A generalization of the {Schwarz--Christoffel} formula},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {109--117},
     publisher = {mathdoc},
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     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2010_13_4_a9/}
}
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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/