@article{oai:u-fukui.repo.nii.ac.jp:02000110,
 author = {Hasegawa, Takemitsu and Sugiura, Hiroshi},
 journal = {Journal of Computational and Applied Mathematics},
 month = {Feb},
 note = {For the integral of a function f over a semi-infinite interval ［0.∞)  with f(x) decaying exponentially as x→∞ , an automatic quadrature scheme is constructed and implemented in Matlab. Three limit formulae of Clenshaw–Curtis-type rules in our recent work (Numerical Algorithms, vol.90, 2022, pp.3–30) are exploited that converge fast for analytic functions. Each formula is expressed by a weighted infinite sum of function values at nodes and so its truncated finite sum is used. The best of the three formulae in accuracy is used as an approximation whose error is estimated with other two formulae and no additional function evaluations, since nodes of the other formulae are included in those of the best one. Numerical results indicate that our automatic scheme is better in performance than the QUADPACK routine for several types of test integrals. Particularly, it copes quite well with oscillatory integrals including the sinusoidal function and/or the Bessel function that are known to be difficult to approximate.},
 title = {An automatic quadrature method for semi-infinite integrals of exponentially decaying functions and its Matlab code},
 volume = {437},
 year = {2024}
}