small argument

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31: 3.5 Quadrature

… ►In particular, when $k=\mathrm{\infty }$ the error term is an exponentially-small function of $1/h$, and in these circumstances the composite trapezoidal rule is exceptionally efficient. … ►Agreement is very good for small values of $t$, but not for larger values. … ►A frequent problem with contour integrals is heavy cancellation, which occurs especially when the value of the integral is exponentially small compared with the maximum absolute value of the integrand. … ►When $\lambda$ is large the integral becomes exponentially small, and application of the quadrature rule of §3.5(viii) is useless. … ►A second example is provided in Gil et al. (2001), where the method of contour integration is used to evaluate Scorer functions of complex argument (§9.12). …