We here present a bivariate Chebyshev series method for the approximation of the experimental frequency and temperature dependent dielectric functions of materials. Within the framework of this method, the dielectric properties are modeled as a low-degree polynomial of the temperature variable (T), the coefficients of which have a frequency (variable f) dependency. This model is then rephrased in terms of the temperature coefficients which are given here as the rational functions of frequency. The principal merits of this method are that it produces a near-best polynomial approximation to the target function, rapidly improves with the order of approximation, and is easy to compute. The favorable features of our approach are demonstrated by considering the experimental wideband Cole-Cole models of animal tissues with the temperature-dependent parameters. The numerical results show the inferiority of the commonly used power-of-f representation of the polynomials concerned due to large rounding errors when the frequency range is large. This problem is ameliorated by expressing the appertaining coefficients as polynomials in the transformed frequency variable x(f) in the Chebyshev basis. Areas of application of the results of this article include the modeling of human exposure to radiofrequency fields, development of treatment and diagnostic procedures, and food processing technologies.
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