Vol. 59, No. 1, 1975

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Generalized axisymmetric elliptic functions

Peter A. McCoy

Vol. 59 (1975), No. 1, 211–221
Abstract

A generalized axisymmetric elliptic function (GASE) Ψν : Ω En C of order ν 0 solving the partial differential equation

         ∂2Ψν-  ∂2Ψ-ν  2ν-∂Ψν-      ∂Ψν-
ℒν(Ψ ν) ≡ ∂x2 +  ∂ρ2 +  ρ  ∂ρ + a(x)∂x  + c(x )Ψ ν = 0
(1)

with analytic coefficients is subject to Cauchy data: Ψν(x,0) = f(x),(∂∕∂ρ)(Ψν(x,0)) = 0 along the singular line. These GASE may be generated from associated analytic functions of one complex variable or associated solutions to the corresponding nonsingular equation by certain integral operators. Convexity arguments geometrically characterize the values of GASE from those of the associates and kernel functions of the respective operators.

Mathematical Subject Classification 2000
Primary: 31B35
Secondary: 35Q05
Milestones
Received: 22 February 1974
Revised: 7 March 1975
Published: 1 July 1975
Authors
Peter A. McCoy