Separation-of-variables solution from the Schwarz-Christoffel transformation

Author:
W. B. Joyce

Journal:
Quart. Appl. Math. **28** (1970), 383-390

DOI:
https://doi.org/10.1090/qam/99785

MathSciNet review:
QAM99785

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References | Additional Information

**[1]**W. R. Smythe,*Static and dynamic electricity*, 3rd ed., McGraw-Hill, New York, 1968**[2]**E. Durand,*Électrostatique*, Vol. II, Masson, Paris, 1966.**[3]**W. K. H. Panofsky and M. Phillips,*Classical electricity and magnetism*, 2nd ed., Addison-Wesley, Reading, Mass., 1962 MR**0135824****[4]**W. K. H. Panofsky and M. Phillips,*Classical electricity and magnetism*, 2nd ed., Addison-Wesley, Reading, Mass., 1962, p. 69 MR**0135824****[5]**K. J. Binns and P. J. Lawrenson,*Electric and magnetic field problems*, Macmillan, New York, 1963, pp. 194 and 235**[6]**G. F. Carrier, M. Krook and C. E. Pearson,*Functions of a complex variable*, McGraw-Hill, New York, 1966 MR**0222256****[7]**V. I. Smirnov,*A course of higher mathematics*, Vol. III, Part II:*Complex variables*.*Special functions*, GITTL, Moscow, 1951; English transl., Pergamon Press, New York and Addison-Wesley, Reading, Mass., 1964, pp. 97 and 147 MR**0182690****[8]**L. V. Kantorovič and V. I. Krylov,*Approximate methods of higher analysis*, Fizmatgiz, Moscow, 1962; English transl., Interscience, New York, 1958, pp. 523-542 MR**0106537****[9]**P. P. Kufarev,*On the method of numerical determination of the parameters in the Schwarz-Christoffel integral*, Dokl. Akad. Nauk SSSR**57**, 535-537 (1947) (Russian) MR**0022911****[10]**M. Abramowitz and I. A. Stegun (Editors) 5th printing with corrections,*Handbook of mathematical functions with graphs, and mathematical tables*, Nat. Bur. Standards Appl. Math. Ser., vol. 55, U. S. Government Printing Office, Washington, D. C., 1966, Eq. 15.3.1 MR**0208798****[11]**I. Stakgold,*Boundary value problems of mathematical physics*, Vol. II, Macmillan, New York, 1968, pp. 164-165; 170 (cf. pp. 272-273) MR**0243183****[12]**W. B. Joyce and S. H. Wemple,*Steady-state junction-current distributions in thin resistive films on semiconductor junctions*(*solutions of*), J. Appl. Phys.**41**, 3818-3830 (1970)**[13]**Further discussions of asymptotic solutions near corners appear in: J. A. Lewis and E. Wasserstrom,*The field singularity at the edge of an electrode on a semiconductor surface*, Bell System Tech. J.**49**, 1183-94 (1970); S. R. Lehman,*Developments at an analytic corner of solutions of elliptic partial differential equations*, J. Math. Mech.**8**, 727-760 (1959); W. R. Wasow,*Asymptotic development of the solution of Dirichlet's problem at analytic corners*, Duke Math. J.**24**, 47-56 (1957).

Additional Information

DOI:
https://doi.org/10.1090/qam/99785

Article copyright:
© Copyright 1970
American Mathematical Society