Bilateral Generating Relations Involving Generalized k-Cesaro Polynomials and k-Lauricella Functions
DOI:
https://doi.org/10.65135/atsf.2026.20Keywords:
Generalized k-Cesaro polynomials, generating functions, k-Lauricella functionsAbstract
In this paper, we introduce a class of k-Lauricella functions by means of the generalized k-Lauricella function and investigate some of their fundamental properties. Using these functions, we derive several families of bilateral generating relations involving the generalized k-Cesaro polynomials and the k-Lauricella functions. The obtained results establish new links between these families of k-special functions and generalize a variety of known generating function identities. Several special cases are also discussed. In particular, it is shown that the classical generating relations associated with generalized Cesaro polynomials and Lauricella functions are recovered when k=1. Hence, the results presented here constitute natural k-extensions of their classical counterparts.
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