In the first part of this work, we derive compact numerical quadrature formulas for finite-range integrals $I[f]=\int^{b}_{a}f(x)\,dx$ , where f ( x )= g ( x )| x t | β , β being real. Depending on the value of β , these integrals are defined either in the regular ...
Quadrature formulas are obtained for the Fourier and Bessel transforms which correspond to the well-known Gauss-Laguerre formula for the Laplace transform. These formulas provide effective asymptotic approximations, complete with error bounds. ...
The authors first present a class of expansions in a series of Bernoulli polyomials and then show how this general result can be applied to yield various (known or new) polynomial expansions. The corresponding expansion problem involving the Euler ...
Association for Computing Machinery
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