Some new uses of the η m ( Z ) functions

Abstract We present a procedure and a MATHEMATICA code for the conversion of formulae expressed in terms of the trigonometric functions sin (ω x), cos (ω x) or hyperbolic functions sinh (λ x), cosh (λ x) 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 undetermin... Title of program: formConv Catalogue Id: AEFB_v1_0 Nature of problem Conversion in terms of the Η m (Z) functions and full elimination of the 0/0 undeterminacy in the coefficients of approximation rules derived in the frame of the exponential fitting. Versions of this program held in the CPC repository in Mendeley Data AEFB_v1_0; formConv; 10.1016/j.cpc.2009.08.007 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)本论文提出了一种将涉及正弦函数sin(ωx)、余弦函数cos(ωx)或双曲函数sinh(λx)、双曲余弦函数cosh(λx)表达的公式转换为以η_m(Z)函数形式表达的方法及其MATHEMATICA代码。此类转换在评估基于指数拟合框架推导出的近似规则系数时具有重要意义。转换后的表达式能够实现诸多功能，其中之一即为完全消除在指数拟合框架下推导出的近似规则系数中的0/0不定性。