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Published online by Cambridge University Press: 20 January 2009
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).
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
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