### Abstract

Original language | English |
---|---|

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

*Journal of Classical Analysis*,

*3*(1), 1-15.

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*Journal of Classical Analysis*, vol. 3, no. 1, pp. 1-15.

**Asymptotics of the Gauss hypergeometric function with large parameters, II.** / Paris, Richard B.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Asymptotics of the Gauss hypergeometric function with large parameters, II

AU - Paris, Richard B.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

M3 - Article

VL - 3

SP - 1

EP - 15

JO - Journal of Classical Analysis

JF - Journal of Classical Analysis

SN - 1848-5987

IS - 1

ER -