Abstract
| Original language | English |
|---|---|
| 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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On the use of Hadamard expansions in hyperasymptotic evaluation : differential equations of hypergeometric type. / Kaminski, D.; Paris, Richard B.
In: Proceedings of the Royal Societ of Edinburgh: Section A Mathematics, Vol. 134, No. 1, 2004, p. 59-178.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 -