Error bounds for the laplace approximation for definite integrals

  title={Error bounds for the laplace approximation for definite integrals},
  author={Frank W. J. Olver},
  journal={Journal of Approximation Theory},
  • F. Olver
  • Published 1968
  • Mathematics
  • Journal of Approximation Theory
Abstract Explicit error bounds are obtained for the well-known asymptotic expansion of integrals of the form ∫ab e−λp(x)q(x)dx, in which λ is a large positive parameter, p(x) and q(x) are real differentiable functions, and p′(x) has a simple zero in the finite or infinite range [a, b]. The bounds are expressed in terms of the supremum of a certain function, taken over [a, b], and are asymptotic to the absolute value of the first neglected term in the expansion, as λ → ∞. Several illustrative… Expand
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  • Mathematics
  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 2015
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