Geodesic
Theorems on the Convergence of Series in Generalized Lommel-Wright Functions
Fractional calculus and applied analysis, Tome 10 (2007) no. 1, pp. 59-74

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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.
Keywords: Bessel, Bessel-Maitland, Generalized Bessel-Maitland, Wright, Generalized Lommel-Wright Functions, Cauchy-Hadamard, Abel and Tauber Theorems, 30B10, 30B30, 33C10, 33C20 
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Paneva-Konovska, Jordanka. Theorems on the Convergence of Series in Generalized Lommel-Wright Functions. Fractional calculus and applied analysis, Tome 10 (2007) no. 1, pp. 59-74. http://geodesic.mathdoc.fr/item/FCAA_2007_10_1_a3/