On the use of Hadamard expansions in hyperasymptotic evaluation: differential equations of hypergeometric type
Published online by Cambridge University Press: 12 July 2007
Abstract
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.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 1 , February 2004 , pp. 159 - 178
- Copyright
- Copyright © Royal Society of Edinburgh 2004
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