Some new uses of the ηm(Z)ηm(Z) functions

We present a procedure and a MATHEMATICA code for the conversion of formulae expressed in terms of the trigonometric functions sin(ωx)sin(ωx), cos(ωx)cos(ωx) or hyperbolic functions sinh(λx)sinh(λx), cosh(λx)cosh(λx) to forms expressed in terms of ηm(Z)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.Program summaryProgram title: formConvCatalogue identifier: AEFB_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFB_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence:http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 596No. of bytes in distributed program, including test data, etc.: 5000Distribution format: tar.gzProgramming language: MathematicaComputer: GenericOperating system: GenericRAM: 15 MBClassification: 5Nature of problem:   Conversion in terms of the ηm(Z)ηm(Z) functions and full elimination of the 0/0 undeterminacy in the coefficients of approximation rules derived in the frame of the exponential fitting.Solution method: Analytic algebraic manipulationRunning time: A few secondsReferences:[1]L.Gr. Ixaru, Numerical Methods for Differential Equations and Applications, Reidel, Dordrecht, Boston, Lancaster, 1984.