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

Paneva-Konovska, Jordanka. "Theorems on the Convergence of Series in Generalized Lommel-Wright Functions." Fractional Calculus and Applied Analysis 10.1 (2007): 59-74. <http://eudml.org/doc/11298>.

@article{Paneva2007,
abstract = {Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20The 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.},
author = {Paneva-Konovska, Jordanka},
journal = {Fractional Calculus and Applied Analysis},
keywords = {30B10; 30B30; 33C10; 33C20},
language = {eng},
number = {1},
pages = {59-74},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Theorems on the Convergence of Series in Generalized Lommel-Wright Functions},
url = {http://eudml.org/doc/11298},
volume = {10},
year = {2007},
}

TY - JOUR
AU - Paneva-Konovska, Jordanka
TI - Theorems on the Convergence of Series in Generalized Lommel-Wright Functions
JO - Fractional Calculus and Applied Analysis
PY - 2007
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 10
IS - 1
SP - 59
EP - 74
AB - Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20The 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.
LA - eng
KW - 30B10; 30B30; 33C10; 33C20
UR - http://eudml.org/doc/11298
ER -