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We analyze the Schwarz–Christoffel mapping with emphasis on its geometric properties and apply it to give an algorithm for numerical computation of the modulus of a polygonal quadrilateral. We represent the generalized modulus of the quadrilaterals by formal power series and give an algorithm for the computation of its coefficients by a hypergeometric function in a special case. To illustrate the effectiveness of the algorithm some computational results are given.
Computational Methods and Function Theory – Springer Journals
Published: Mar 1, 2024
Keywords: Schwarz–Christoffel mapping; Hypergeometric function; Quadrilateral; Conformal modulus; 30C62; 33E05
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