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- W2028528602 abstract "The purpose of this paper is to extend the MIPS theory described in Parts I and II to functions having algebraic singularities. As in the simpler cases, the theory is based on expressing the remainder term in the appropriate Fourier coefficient asymptotic expansion as an infinite series, each element of which is a remainder in the Euler-Maclaurin summation formula. In this way, an expression is found for f' f(x) cos 2irmx dx (O 5 a -1. This expression, and variants of it form a convenient basis for the numerical calculation of a set of Fourier coefficients. The calculation requires approximate values of the first few derivatives of +(x) at x = a and at x = b, together with trapezoidal rule sums over (0, 1) of f(). Some of the incidental constants are values of the generalized zeta function t(s, a). 1. Outline of Problem. In Parts I and II (Lyness (1), (2)) of this series, the author has introduced representations for the Fourier coefficients" @default.
- W2028528602 created "2016-06-24" @default.
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- W2028528602 date "1971-09-01" @default.
- W2028528602 modified "2023-09-26" @default.
- W2028528602 title "The calculation of Fourier coefficients by the Möbius inversion of the Poisson summation formula. III. Functions having algebraic singularities" @default.
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- W2028528602 doi "https://doi.org/10.1090/s0025-5718-1971-0297162-6" @default.
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