A family of numerical quadrature formulas is introduced by application of the trapezoidal rule to infinite integrals which result from the given integrals ∫^b_a f(x)dx by suitable variable transformations x = φ(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.
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Takahasi et al. (1973) studied this question.
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