Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Second-Order Differential Equations with Fractional Transition Points

F. W. J. Olver
Transactions of the American Mathematical Society
Vol. 226 (Feb., 1977), pp. 227-241
DOI: 10.2307/1997952
Stable URL: http://www.jstor.org/stable/1997952
Page Count: 15
  • Read Online (Free)
  • Download ($30.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Second-Order Differential Equations with Fractional Transition Points
Preview not available

Abstract

An investigation is made of the differential equation $$d^2w/dx^2 = \{u^2(x - x_0)^\lambda f(u, x) + g(u, x)/(x - x_0)^2\}w$$, in which $u$ is a large real (or complex) parameter, $\lambda$ is a real constant such that $\lambda > -2, x$ is a real (or complex) variable, and $f(u, x)$ and $g(u, x)$ are continuous (or analytic) functions of $x$ in a real interval (or complex domain) containing $x_0$. The interval (or domain) need not be bounded. Previous results of Langer and Riekstiņš giving approximate solutions in terms of Bessel functions of order $1/(\lambda + 2)$ are extended and error bounds supplied.

Page Thumbnails

  • Thumbnail: Page 
227
    227
  • Thumbnail: Page 
228
    228
  • Thumbnail: Page 
229
    229
  • Thumbnail: Page 
230
    230
  • Thumbnail: Page 
231
    231
  • Thumbnail: Page 
232
    232
  • Thumbnail: Page 
233
    233
  • Thumbnail: Page 
234
    234
  • Thumbnail: Page 
235
    235
  • Thumbnail: Page 
236
    236
  • Thumbnail: Page 
237
    237
  • Thumbnail: Page 
238
    238
  • Thumbnail: Page 
239
    239
  • Thumbnail: Page 
240
    240
  • Thumbnail: Page 
241
    241