Numerical Calculation of Certain Definite Integrals by Poisson's Summation Formula
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چکیده
It is generally agreed that of all quadrature formulae, the trapezoidal rule, while being the simplest, is also the least accurate. There is, however, a rather general class of integrals for which the trapezoidal rule can be shown to be a highly accurate means of obtaining numerical values. Specifically, if the integrand is a periodic, even function with all derivatives continuous, then the integral over a period is given by the trapezoidal rule with high precision. Similarly, integrals
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Numerical Calculation of Certain Definite Integrals by Poisson's Summation Formula
It is generally agreed that of all quadrature formulae, the trapezoidal rule, while being the simplest, is also the least accurate. There is, however, a rather general class of integrals for which the trapezoidal rule can be shown to be a highly accurate means of obtaining numerical values. Specifically, if the integrand is a periodic, even function with all derivatives continuous, then the int...
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