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Finite difference formulas and numerical contour integration in the complex plane

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CATW04 - Complex analysis: techniques, applications and computations - perspectives in 2023

In many applications, function values are available only at equispaced grid points. In the case of analytic functions and grids in the complex plane, 2-D finite difference formulas become remarkably accurate already for very small stencil sizes. Their use in place of analytic derivatives in the Euler-Maclaurin formula results in highly effective computational methods for both contour integration and for numerical evaluation of fractional derivatives.

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