Sekatskii, Sergey2023-02-272023-02-272023-02-272023-01-0110.3390/axioms12010068https://infoscience.epfl.ch/handle/20.500.14299/195176WOS:000919535400001Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of an analytical function to obtain a few new criteria equivalent to the Riemann hypothesis. Here, the same theorem is applied to calculate certain infinite sums and study the properties of zeroes of a few analytical functions. On many occasions, this enables to facilitate the obtaining of known results thus having important methodological meaning. Additionally, some new results, to the best of our knowledge, are also obtained in this way. For example, we established new properties of the sum of inverse zeroes of a digamma function, new formulae for the sums Sigma(ki) (2)(p)(i) for zeroes r i of incomplete gamma and Riemann zeta functions having the order ki (These results can be straightforwardly generalized for the sums Sigma(ki)/p(i)(n) with integer n > 2, and so on.)Mathematics, AppliedMathematicsgeneralized littlewood theoremlogarithm of an analytical functionzeroes and poles of analytical functioninfinite sumsriemann zeta-functiontext::journal::journal article::research article