Some new uses of the η m (Z) functions. We present a procedure and a MATHEMATICA code for the conversion of formulae expressed in terms of the trigonometric functions sin(ωx), cos(ωx) or hyperbolic functions sinh(λx), cosh(λx) to forms expressed in terms of η m (Z) functions. The possibility of such a conversion is important in the evaluation of the coefficients of the approximation rules derived in the frame of the exponential fitting. The converted expressions allow, among others, a full elimination of the 0/0 undeterminacy, uniform accuracy in the computation of the coefficients, and an extended area of validity for the corresponding approximation formulae.
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References in zbMATH (referenced in 5 articles )
Showing results 1 to 5 of 5.
- Conte, Dajana; Paternoster, Beatrice: Modified Gauss-Laguerre exponential fitting based formulae (2016)
- Conte, Dajana; Ixaru, Liviu Gr.; Paternoster, Beatrice; Santomauro, Giuseppe: Exponentially-fitted Gauss-Laguerre quadrature rule for integrals over an unbounded interval (2014)
- D’Ambrosio, Raffaele; Esposito, Elena; Paternoster, Beatrice: Exponentially fitted two-step Runge-Kutta methods: construction and parameter selection (2012)
- Paternoster, Beatrice: Present state-of-the-art in exponential fitting. A contribution dedicated to Liviu Ixaru on his 70th birthday (2012)
- Conte, D.; Esposito, E.; Paternoster, B.; Ixaru, L.Gr.: Some new uses of the $\eta _m(Z)$ functions (2010)