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 need an accessible version of this item please contact JSTOR User Support

Gamma Function Asymptotics by an Extension of the Method of Steepest Descents

W. G. C. Boyd
Proceedings: Mathematical and Physical Sciences
Vol. 447, No. 1931 (Dec. 8, 1994), pp. 609-630
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/52450
Page Count: 22
  • Get Access
  • Read Online (Free)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Gamma Function Asymptotics by an Extension of the Method of Steepest Descents
Preview not available

Abstract

Recent work of Berry & Howls, which reformulated the method of steepest descents, is exploited to derive a new representation for the gamma function. It is shown how this representation can be used to derive a number of properties of the asymptotic expansion of the gamma function, including explicit and realistic error bounds, the Berry transition between different asymptotic representations across a Stokes line, and asymptotic estimates for the late coefficients.

Page Thumbnails

  • Thumbnail: Page 
609
    609
  • Thumbnail: Page 
610
    610
  • Thumbnail: Page 
611
    611
  • Thumbnail: Page 
612
    612
  • Thumbnail: Page 
613
    613
  • Thumbnail: Page 
614
    614
  • Thumbnail: Page 
615
    615
  • Thumbnail: Page 
616
    616
  • Thumbnail: Page 
617
    617
  • Thumbnail: Page 
618
    618
  • Thumbnail: Page 
619
    619
  • Thumbnail: Page 
620
    620
  • Thumbnail: Page 
621
    621
  • Thumbnail: Page 
622
    622
  • Thumbnail: Page 
623
    623
  • Thumbnail: Page 
624
    624
  • Thumbnail: Page 
625
    625
  • Thumbnail: Page 
626
    626
  • Thumbnail: Page 
627
    627
  • Thumbnail: Page 
628
    628
  • Thumbnail: Page 
629
    629
  • Thumbnail: Page 
630
    630