Theorems on the Convergence of Series in Generalized Lommel-Wright Functions

Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20

The classical Cauchy-Hadamard, Abel and Tauber theorems provide useful information on the convergence of the power series in complex plane. In this paper we prove analogous theorems for series in the generalized Lommel-Wright functions with 4 indices. Results for interesting special cases of series involving Bessel, Bessel-Maitland, Lommel and Struve functions, are derived.We provide also a new asymptotic formula for the generalized Lommel-Wright functions in the case of large values of the index ν that are used in the proofs of the Cauchy-Hadamard, Abel and Tauber type theorems for the considered series.

* This work is partially supported by National Science Research Fund - Bulgarian Ministry of Education and Science, under Grant MM 1305/2003.