Hostname: page-component-5b777bbd6c-2c8nx Total loading time: 0 Render date: 2025-06-18T21:30:52.037Z Has data issue: false hasContentIssue false
  • English
  • Français

The real zeros of the confluent hypergeometric function

Published online by Cambridge University Press:  24 October 2008

L. J. Slater
L. J. Slater
Affiliation:
University Mathematical Laboratory Corn Exchange Street Cambridge
Get access Rights & Permissions [Opens in a new window]

Extract

This paper contains a discussion of various points which arise in the numerical evaluation of the small real zeros of the confluent hypergeometric function

where

There are two distinct problems, first the determination of those values of x for which M(a, b; x) = 0, given a and b, and secondly the study of the curves represented by M (a, b; x) = 0, for fixed values of x. These curves all lie on the surface M(a, b; x) = 0, of course.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 52 , Issue 4 , October 1956 , pp. 626 - 635
Copyright
Copyright © Cambridge Philosophical Society 1956

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

(1) Buchholz, H. Die Konfluente Hypergeometrische funktion (Berlin, 1953).Google Scholar
(2) Erdelyi, A. Higher Transcendental Functions, Vol. 1 (Bateman project, 1953).Google Scholar
(3) Miller, J. C. P. The Airy Integral. British Association Mathematical Tables, Part Vol. B (Cambridge, 1946).Google Scholar
(4) Slater, L. J. On the evaluation of the confluent hypergeometric function. Proc. Camb. Phil. Soc. 49 (1953), 612–22.Google Scholar
(5) Tricomi, F. G. Funzioni Ipergeometriche Confluenti (Rome, 1954).Google Scholar
(6) Whittaker, E. T. and Watson, G. N. Modern Analysis, 4th ed. (Cambridge, 1946.)Google Scholar