Summation of trigonometric series by methods with power multiplier

Abstract

The methods of power summation of factors, degree of factors which are arbitrary powers of summation
indices are reviewed. It is shown that by Poisson-Abel method only those series can be
summarized the order of member increase of which is proportional to the exponent depending on
the summation index. Gauss-Weierstrass method and other power factors methods can be also
applied to the series the terms of which increase in proportion to the exponential dependence of
the indices summation.