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On an Asymptotic Expansion of the Hypergeometric Function

Published online by Cambridge University Press:  20 January 2009

T. M. MacRobert
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In a previous paper the author has employed the expansion

where

and

to establish the theorem that, if −π/2<amp γ<π/2, the function Ps/Ts+1 remains finite as γ→∞. This theorem is valid provided that z is not real and ≧ 1.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , February 1923 , pp. 84 - 87
Copyright
Copyright © Edinburgh Mathematical Society 1923

References

* Proc. Edin. Math. Soc., Vol. XLI, pp. 82–92.

† R(γ) and s are taken so large that R(γ−β)>0 and R(β+s)>0.

‡ Cf. Watson, G. N., Trans. Camb. Phil. Soc., Vol. 22, 1918, p. 299.Google Scholar