### Abstract

Original language | English |
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Pages (from-to) | 59-178 |

Number of pages | 20 |

Journal | Proceedings of the Royal Societ of Edinburgh: Section A Mathematics |

Volume | 134 |

Issue number | 1 |

DOIs | |

State | Published - 2004 |

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### Cite this

*Proceedings of the Royal Societ of Edinburgh: Section A Mathematics*,

*134*(1), 59-178. DOI: 10.1017/S0308210500003139

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*Proceedings of the Royal Societ of Edinburgh: Section A Mathematics*, vol 134, no. 1, pp. 59-178. DOI: 10.1017/S0308210500003139

**On the use of Hadamard expansions in hyperasymptotic evaluation : differential equations of hypergeometric type.** / Kaminski, D.; Paris, Richard B.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the use of Hadamard expansions in hyperasymptotic evaluation

T2 - Proceedings of the Royal Societ of Edinburgh: Section A Mathematics

AU - Kaminski,D.

AU - Paris,Richard B.

PY - 2004

Y1 - 2004

N2 - We describe how a modification of a common technique for developing asymptotic expansions of solutions of linear differential equations can be used to derive Hadamard expansions of solutions of differential equations. Hadamard expansions are convergent series that share some of the features of hyperasymptotic expansions, particularly that of having exponentially small remainders when truncated, and, as a consequence, provide a useful computational tool for evaluating special functions. The methods we discuss can be applied to linear differential equations of hypergeometric type and may have wider applicability.

AB - We describe how a modification of a common technique for developing asymptotic expansions of solutions of linear differential equations can be used to derive Hadamard expansions of solutions of differential equations. Hadamard expansions are convergent series that share some of the features of hyperasymptotic expansions, particularly that of having exponentially small remainders when truncated, and, as a consequence, provide a useful computational tool for evaluating special functions. The methods we discuss can be applied to linear differential equations of hypergeometric type and may have wider applicability.

U2 - 10.1017/S0308210500003139

DO - 10.1017/S0308210500003139

M3 - Article

VL - 134

SP - 59

EP - 178

JO - Proceedings of the Royal Societ of Edinburgh: Section A Mathematics

JF - Proceedings of the Royal Societ of Edinburgh: Section A Mathematics

SN - 1473-7124

IS - 1

ER -