Computational Methods and Function Theory 7 (2007), No. 1, 293--308
Copyright Heldermann Verlag 2007
Darren G. Crowdy
d.crowdy@imperial.ac.uk , Imperial College London, Department of Mathematics, 180 Queen's Gate, London, SW7 2AZ, U.K.
Jonathan S. Marshall
jonathan.marshall@imperial.ac.uk , Imperial College London, Department of Mathematics, 180 Queen's Gate, London, SW7 2AZ, U.K.
A numerical algorithm is presented for the computation of the Schottky-Klein prime function on the Schottky double of multiply connected circular domains in the plane. While there exist classical formulae for the Schottky-Klein prime function in the form of infinite products over a Schottky group, such products are not convergent for all choices of multiply connected circular domains. The prime function itself, however, is a well-defined function for any multiply connected circular domain. The present algorithm facilitates the evaluation of this prime function when the planar domains are such that the classical infinite product representation is either not convergent or so slowly convergent as to be impracticable.
Keywords: Schottky-Klein prime function, Schottky double, multiply connected.
MSC 2000: 30F10, 30F15.
[FullText-pdf (335 K)] [FullText-ps (486 K)]