# Error bounds for the laplace approximation for definite integrals

@article{Olver1968ErrorBF, title={Error bounds for the laplace approximation for definite integrals}, author={F. Olver}, journal={Journal of Approximation Theory}, year={1968}, volume={1}, pages={293-313} }

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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