Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

A procedure for conformal maps of simply connected domains by using the Bergman function


Author: J. Burbea
Journal: Math. Comp. 24 (1970), 821-829
MSC: Primary 68.00
DOI: https://doi.org/10.1090/S0025-5718-1970-0277138-4
MathSciNet review: 0277138
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Conformal maps of simply connected domains onto the unit circle are computed by means of the Bergman function of the domain. Ellipses and squares are mapped by this method. Further various parameters of the Schwarz-Christoffel formula are computed in terms of the Bergman function.


References [Enhancements On Off] (What's this?)

  • [1] S. Bergman, The Kernel Function and Conformal Mapping, Math. Surveys, no. 5, Amer. Math. Soc., Providence, R. I., 1950. MR 12, 402. MR 0038439 (12:402a)
  • [2] S. Bergman & B. Chalmers, "A procedure of conformal mapping of triply-connected domains," Math. Comp., v. 21, 1967, pp. 527-542. MR 37 #4243a. MR 0228663 (37:4243a)
  • [3] P. Davis & P. Rabinowitz, "Abscissas and weights for Gaussian quadratures of high order," J. Res. Nat. Bur. Standards Sect. B, v. 56, 1965, pp. 35-37. MR 0076463 (17:902g)
  • [4] D. Gaier, Konstruktive Methoden der konformen Abbildung, Springer Tracts in Natural Philosophy, vol. 3, Springer-Verlag, Berlin, 1964. MR 33 #7507. MR 0199360 (33:7507)
  • [5] Z. Nehari, Conformal Mapping, McGraw-Hill, New York, 1952. MR 13, 640. MR 0045823 (13:640h)
  • [6] P. Rabinowitz, "Numerical experiments in conformal mapping by the method of orthonormal polynomials," J. Assoc. Comput. Mach., v. 13, 1966, pp. 296-303.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 68.00

Retrieve articles in all journals with MSC: 68.00


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1970-0277138-4
Keywords: Bergman kernel function, conformal maps, reproducing property, Gaussian quadrature rule
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society