An alternative method to obtain integral kernels for Lamé integral equations

In the present paper we introduce an alternative approach to obtain kernels for Lamé integral equations. The introduced procedure, based solely on simple algebraic manipulations, furnishes the well known kernels of hypergeometric form in an almost trivial manner without the use of transformations. More important, it provides a set of novel nuclei for Lamé integral equations in the form of Heun functions.