On series involving zeros of trascendental functions arising from Volterra integral equations

Abstract

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.

Keywords

• Sum of series
• Trascendental functions
• Laplace transforms.