A continued-fraction-based multi-point Padé method converts the Laplace transform of a target function into coefficients and poles that yield an exponential-sum approximation on R+.
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New approximations to the Riemann zeta function and its derivative are created by approximating the remainder term of the Riemann-Siegel formula with elementary functions and Gaussian quadrature coefficients, backed by numerical tests.
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Approximating functions on ${\mathbb R}^+$ by exponential sums
A continued-fraction-based multi-point Padé method converts the Laplace transform of a target function into coefficients and poles that yield an exponential-sum approximation on R+.
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Simple and accurate approximations to the Riemann zeta function
New approximations to the Riemann zeta function and its derivative are created by approximating the remainder term of the Riemann-Siegel formula with elementary functions and Gaussian quadrature coefficients, backed by numerical tests.