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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 = (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.
Takahasi et al. (Mon,) studied this question.