Asymptotic approximations of the Apostol-tangent numbers and polynomials were established for non-zero complex values of the parameter λ. Fourier expansion of the Apostol-tangent polynomials was used to obtain the asymptotic approximations. The asymptotic formulas for the cases λ=1 and λ=−1 were explicitly considered to obtain asymptotic approximations of the corresponding tangent numbers and polynomials.
The subject of the research is the control algorithms for a seven-phase converter that implement space-vector voltage modulation of a seven-phase motor as an alternative to a three-phase engine in modern electric traction. The study used elements of set theory, combinatorics, Fourier series expansion and vector analysis. Checking research results was implemented on a special stand for experimental studies of spatial vector voltage modulation of a seven-phase motor.
Asymptotic Approximation of the Apostol-Tangent Polynomials Using Fourier Series
