Jovan D. Kečkić

Master’s dissertation of J. V. Sohocki

This section is devoted to Master’s dissertation of the Russian mathematician J. V. Sohocki which was published under the title The theory of integral residues with some applications (Russian), St. Petersbourg 1868, VIII+135 pp.

Applications of Calculus of Residues to Special Functions

The polygamma functions Ψ (n) are defined for nonnegative integers n by

Evaluation of Residues

{\psi ^{\left( n \right)}}\left( x \right) = {\left( {\frac{d}{{dx}}} \right)^{n + 1}}\log \Gamma \left( x \right).

The Cauchy method of residues : theory and applications

Suppose that k and n are positive integers and let

The Cauchy Method of Residues Volume 2

{T_k} = \exp \left( {\frac{{2\pi i{k^2}}}{n}} \right)