JournalsprimsVol. 9, No. 3pp. 721–741

Double Exponential Formulas for Numerical Integration

  • Hidetosi Takahasi

    University of Tokyo, Japan
  • Masatake Mori

    Tokyo Denki University, Japan
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Abstract

A family of numerical quadrature formulas is introduced by application of the trapezoidal rule to infinite integrals which result from the given integrals  ∫ ba f(x)dx by suitable variable transformations x = ø(u). These formulas are characterized by having double exponential asymptotic behavior of the integrands in the resulting infinite integrals as u → ± ∞, and it is shown both analytically and numerically that such formulas are generally optimal with respect to the ecomony of the number of sampling points.

Cite this article

Hidetosi Takahasi, Masatake Mori, Double Exponential Formulas for Numerical Integration. Publ. Res. Inst. Math. Sci. 9 (1973), no. 3, pp. 721–741

DOI 10.2977/PRIMS/1195192451