### Abstract

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

Pages (from-to) | 3024-3034 |

Number of pages | 11 |

Journal | Computers & Mathematics with Applications |

Volume | 61 |

Issue number | 19 |

DOIs | |

State | Published - May 2011 |

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### Cite this

*Computers & Mathematics with Applications*,

*61*(19), 3024-3034. DOI: 10.1016/j.camwa.2011.03.092

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*Computers & Mathematics with Applications*, vol 61, no. 19, pp. 3024-3034. DOI: 10.1016/j.camwa.2011.03.092

**The discrete analogue of Laplace’s method.** / Paris, Richard B.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The discrete analogue of Laplace’s method

AU - Paris,Richard B.

PY - 2011/5

Y1 - 2011/5

N2 - We give a justification of the discrete analogue of Laplace’s method applied to the asymptotic estimation of sums consisting of positive terms. The case considered is the series related to the hypergeometric function pFq−1(x) (with q≥p+1) as x→+∞ discussed by Stokes [G.G. Stokes, Note on the determination of arbitrary constants which appear as multipliers of semi-convergent series, Proc. Camb. Phil. Soc. 6 (1889) 362–366]. Two examples are given in which it is shown how higher order terms in the asymptotic expansion may be derived by this procedure.

AB - We give a justification of the discrete analogue of Laplace’s method applied to the asymptotic estimation of sums consisting of positive terms. The case considered is the series related to the hypergeometric function pFq−1(x) (with q≥p+1) as x→+∞ discussed by Stokes [G.G. Stokes, Note on the determination of arbitrary constants which appear as multipliers of semi-convergent series, Proc. Camb. Phil. Soc. 6 (1889) 362–366]. Two examples are given in which it is shown how higher order terms in the asymptotic expansion may be derived by this procedure.

U2 - 10.1016/j.camwa.2011.03.092

DO - 10.1016/j.camwa.2011.03.092

M3 - Article

VL - 61

SP - 3024

EP - 3034

JO - Computers & Mathematics with Applications

T2 - Computers & Mathematics with Applications

JF - Computers & Mathematics with Applications

SN - 0898-1221

IS - 19

ER -