分野別セミナー

Series arising from Volterra integral equations of the second kind are summed. The series involve inverse powers of roots of the characteristic equation. It is shown how previous similar series obtained from differential-difference equations are particular cases of the present development. A number of novel and interesting results are obtained. The techniques are demonstrated through illustrative examples. The application of general techniques to obtain expressions involving the zeros of the Riemann Zeta function is investigated. In particular, novel two parameter expressions are obtained involving the non-trivial zeros of the Zeta function.