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

Recurrence Relations for Hypergeometric Functions of Unit Argument

Stanisław Lewanowicz
Mathematics of Computation
Vol. 45, No. 172 (Oct., 1985), pp. 521-535
DOI: 10.2307/2008142
Stable URL: http://www.jstor.org/stable/2008142
Page Count: 15
  • Read Online (Free)
  • Download ($34.00)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Recurrence Relations for Hypergeometric Functions of Unit Argument
Preview not available

Abstract

We show that the generalized hypergeometric function \begin{equation*}P_n:=_{p + 3}F_{p + 2}\Bigg(\overset{-n, n + \lambda, a_p, 1}{b_{p + 2}} \Bigg| 1\Bigg)\quad (n \geq 0)\end{equation*} satisfies a nonhomogeneous recurrence relation of order $p + \sigma$, where $\sigma = 0$ when $_{p + 3}F_{p + 2}(1)$ is balanced, and $\sigma = 1$ otherwise. Also, for \begin{equation*}U_n:= \frac{(c_{q + 1})_n}{(d_q)_n(n + \lambda)_n}_{q + 2}F_{q + 1}\Bigg(\overset{n + c_{q + 2}}{n + d_q, 2n + \lambda + 1}\Bigg| 1\Bigg)\quad (n \geq 0)\end{equation*} a homogeneous recurrence relation of order $q + 1$ is given.

Page Thumbnails

  • Thumbnail: Page 
521
    521
  • Thumbnail: Page 
522
    522
  • Thumbnail: Page 
523
    523
  • Thumbnail: Page 
524
    524
  • Thumbnail: Page 
525
    525
  • Thumbnail: Page 
526
    526
  • Thumbnail: Page 
527
    527
  • Thumbnail: Page 
528
    528
  • Thumbnail: Page 
529
    529
  • Thumbnail: Page 
530
    530
  • Thumbnail: Page 
531
    531
  • Thumbnail: Page 
532
    532
  • Thumbnail: Page 
533
    533
  • Thumbnail: Page 
534
    534
  • Thumbnail: Page 
535
    535