Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-20T04:00:28.756Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the sums of certain bilateral hypergeometric series

Published online by Cambridge University Press:  24 October 2008

H. S. Shukla
H. S. Shukla
Affiliation:
Department of MathematicsUniversity of LucknowLucknow (India)
Get access Rights & Permissions [Opens in a new window]

Extract

Some years ago M. Jackson(5) obtained the sum of a particular 3H3 series which generalized the theorems of Whipple and Watson on sums of a 3F2 series, and later she(6) deduced the sum of a particular well-poised 6H6( – 1) series. In this note sums of certain particular bilateral hypergeometric series of the same type are given. They are believed to be new. In the sequel, the sum of a particular 8Ψ8 series has been obtained. The existence of a particular case of this sum was pointed out earlier by Slater and Lakin (11).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 55 , Issue 3 , July 1959 , pp. 262 - 266
Copyright
Copyright © Cambridge Philosophical Society 1959

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)Bailey, W. N.Generalized hypergeometric series (Cambridge, 1935).Google Scholar
(2)Bailey, W. N.Quart. J. Math. (Oxford), 7 (1936), 105–15.CrossRefGoogle Scholar
(3)Bailey, W. N.Proc. Lond. Math. Soc. (2) 50 (1948), 1–10.CrossRefGoogle Scholar
(4)Bailey, W. N.Quart. J. Math. (Oxford) (2) (1950), 194–8.CrossRefGoogle Scholar
(5)Jackson, M.J. Lond. Math. Soc. 24 (1949), 238–40.CrossRefGoogle Scholar
(6)Jackson, M.J. Lond. Math. Soc. 27 (1952), 124–6.CrossRefGoogle Scholar
(7)Jackson, M.J. Lond. Math. Soc. 27 (1952), 116–23.CrossRefGoogle Scholar
(8)Jackson, M.Quart. J. Math. (Oxford) (2) 1 (1950), 63–8.CrossRefGoogle Scholar
(9)Jackson, M.Pacific J. Math. 4 (1954), 557–62.CrossRefGoogle Scholar
(10)Slater, L. J.Quart. J. Math. (Oxford) (2) 3 (1952), 72–80.Google Scholar
(11)Slater, L. J. and Lakin, A.Proc. Edinb. Math. Soc. (2) 9 (1956), 116–21.CrossRefGoogle Scholar
(12)Shukla, H. S.Proc. Glasg. Math. Ass. 3 (1957), 141–4.CrossRefGoogle Scholar