### Abstract

We obtain asymptotic expansions by application of the method of steepest descents for the Gauss hypergeometric function F(a+ε1λ,b+ε2λ;c+λ;z) as |λ| → ∞ when 0<ε1 <1 and ε1 >1 where, without loss of generality, it is supposed that ε1 6ε2 . The resulting expansions are of Poincar´e type and break down in the neighbourhood of certain critical points in the z-plane. Numerical results illustrating the accuracy of the different expansions are given.

Original language | English |
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Pages (from-to) | 1-15 |

Number of pages | 15 |

Journal | Journal of Classical Analysis |

Volume | 3 |

Issue number | 1 |

Publication status | Published - 2013 |

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## Cite this

Paris, R. B. (2013). Asymptotics of the Gauss hypergeometric function with large parameters, II.

*Journal of Classical Analysis*,*3*(1), 1-15. http://dx.doi.org/10.7153/jca-03-01