Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-28T04:16:56.641Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the real zeros of the basic confluent hypergeometric function

Published online by Cambridge University Press:  24 October 2008

Ramadhar Mishra
Ramadhar Mishra
Affiliation:
The University, Gorakhpur, India
Get access Rights & Permissions [Opens in a new window]

Extract

Some years back, Slater (4) discussed the approximations, based on the expansion in series, for the cases 1F1(a; b; x) = 0, when either of b and x or a and x are fixed. These approximations were based essentially on the well-known Newton's method of approximation and were helpful in the numerical evaluation of the small real zeros of the confluent hypergeometric function 1F1(a; b; x;). In this note, we deal with the corresponding problem for the basic confluent hypergeometric function 1Φ1(a; b; x;).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 3 , July 1968 , pp. 683 - 686
Copyright
Copyright © Cambridge Philosophical Society 1968

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.)

References

REFERENCES

(1)Hahn, W.Über uneigentliche Lösungen linearer geometrischer Differenzengleichungen, Math. Annalen, 125 (1952), 67–81.CrossRefGoogle Scholar
(2)Jackson, F. H.q-form of Taylor's theorem, Messenger of Math. 38 (1909), 62–64.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.The real zeros of the confluent hypergeometric function, Proc. Cambridge Philos. Soc. 52 (1956), 626–635.CrossRefGoogle Scholar