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Some new uses of the ηm(Z) functions

D. Conte
E. Esposito
Beatrice Paternoster
Organization: Universita' di Salerno
L. Gr. Ixaru
Journal / Anthology

Computer Physics Communications
Year: 2010
Volume: 181
Issue: 1
Page range: 128-137

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 ηm(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.