ABSTRACT
This chapter discusses the classical Abel-type integral equation having a gamma function. It introduces convolution associated with the Mellin transform, and derives an equation, which implies that the Mellin transform of the convolution equals to the product of the Mellin transforms. The chapter also derives calculations that are more stable with respect to small perturbations. It discusses finding of locations and values of jumps of the solution to the Albel-type integral equation. The problem of finding discontinuities of the solution to the Albel-type integral equation is considered. The jumps are mapped into a function which is easily calculated in an analytical manner.
