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A Generalised Hypergeometric Function

Published online by Cambridge University Press:  20 January 2009

William Fabian
William Fabian
Affiliation:
14 Grosvenor Avenue, Canonbury, London, N.5.
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The hypergeometric function1F(a, b; c; z) is analytic in the domain |arg(−z)| < π, and, when |z| < 1, may be represented by the series

When |z| = 1 in the domain |arg(−z)| <π, this series converges2 to F(a; b; c; z) if R(a+b−c) < 0 (integral values of a, b and c are excluded in the present paper).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 9 , Issue 3 , July 1956 , pp. 151 - 153
Copyright
Copyright © Edinburgh Mathematical Society 1956

References

1 Whittaker, and Watson, , Modern Analysis (1927), Ch. XIV.Google Scholar

2 Ibid., pp. 25 and 57.

3 Fabian, , Quart. J. of Math., 7 (1936), 252. CJ. the Riemann-Liouville integral.CrossRefGoogle Scholar

1 Fabian, , Math. Gazette, 20 (1936), 249.CrossRefGoogle Scholar

2 Whittaker, and Watson, , op. cit., p. 23.Google Scholar

1 Fabian, , Math. Gazette, 20 (1936), 249.CrossRefGoogle Scholar