ERROR ESTIMATES FOR DOMINICI’S HERMITE FUNCTION ASYMPTOTIC FORMULA AND SOME APPLICATIONS

Error Estimates for Dominici’s Hermite Function Asymptotic Formula and Some Applications

The aim of this paper is to find a concrete bound for the error involved when approximating the nth Hermite function (in the oscillating range) by an asymptotic formula due to D. Dominici. This bound is then used to study the accuracy of certain approximations to Hermite expansions and to Fourier transforms. A way of estimating an unknown probability density is proposed. 2000 Mathematics subjec...

Asymptotic Error Estimates for the Gauss Quadrature Formula

Asymptotic Coefficients of Hermite Function Series

By using complex variable methods (steepest descent and residues) to asymptotically evaluate the coefftcient integrals, the numerical analysis of Hermite function series is discussed. There are striking similarities and differences with the author’s earlier work on Chebyshev polynomial methods (J. Comp. Phys. 45 (1982), 45-49) for infinite or semi-infinite domains. Like Chebyshev series, the He...

Some new asymptotic approximations of the gamma function based on Nemesâ€TM formula, Ramanujanâ€TMs formula and Burnsideâ€TMs formula

In this paper, we construct some new approximations of the gamma function based on Nemes’ formula, Ramanujan’s formula and Burnside’s formula. Using these approximations, some inequalities are established. Finally, for demonstrating the superiority of our new approximation over Mortici’s formula and other classical ones, some numerical computations are also given. 2014 Elsevier Inc. All rights ...

Error estimates for some quasi-interpolation operators

‖u− Ihu‖L2(T ) ≤cThT ‖∇ku‖L2(ω̃T ), ‖u− Ihu‖L2(E) ≤cEh E ‖∇ku‖L2(ω̃E). Here, k ∈ {1, 2}, Ih is some quasi-interpolation operator, T and E are a simplex and a face thereof, hT and hE measure the size of T and E, and ω̃T and ω̃E are neighbourhoods of T and E which should be as small as possible. Note that the interpolate Ihu never needs to be computed explicitely. Moreover, for problems in two and th...