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Published online by Cambridge University Press: 20 January 2009
Adopting the notation of Barnes1 and Fox, let us write
If q > p — l, the series on the right of (1) represents an integral function, while if q = p — 1, the series converges only inside or on the circle | x |=1.
page 19 note 1Barnes, E. W., Proc. London Math. Soc. (2), 6 (1906), 59–116.Google Scholar
page 19 note 2Fox, C., Proc. London Math. Soc. (2), 26 (1927), 201.CrossRefGoogle Scholar
page 19 note 3Bailey, W. N., Generalized Hypergeometric Series (Cambridge Tract No. 32, 1935), p. 28Google Scholar
page 19 note 4Whipple, F. J. W., Proc. London Math. Soc. (2), 25 (1926), 247–263.CrossRefGoogle Scholar
page 20 note 1 I am indebted to a referee for this suggestion.
page 21 note 1
page 21 note 2Whittaker, E. T. and Watson, G. N., Modern Analysis (Cambridge, 1920), p. 338.Google Scholar
page 21 note 3Whittaker, E. T. and Watson, G. N., Modem Analysis (Cambridge, 1920), p. 360.Google Scholar
page 22 note 1 This is a special case of equation (12) with See Watson, G. N., Bessel Functions (Cambridge, 1922), p. 366.Google Scholar
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