Double Exponential Formulas for Numerical Integration

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  • Double exponential formulas for numerical indefinite integration

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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 ∫abf(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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