Summation of Series over Bourget Functions
Canadian mathematical bulletin, Tome 51 (2008) no. 4, pp. 627-636
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In this paper we derive formulas for summation of series involving J. Bourget's generalization of Bessel functions of integer order, as well as the analogous generalizations by H. M. Srivastava. These series are expressed in terms of the Riemann $\zeta$ function and Dirichlet functions $\eta$ , $\lambda$ , $\beta$ , and can be brought into closed form in certain cases, which means that the infinite series are represented by finite sums.
Mots-clés :
33C10, 11M06, 65B10, Riemann zeta function, Bessel function, Bourget function, Dirichlet function
Vidanović, Mirjana V.; Tričković, Slobodan B.; Stanković, Miomir S. Summation of Series over Bourget Functions. Canadian mathematical bulletin, Tome 51 (2008) no. 4, pp. 627-636. doi: 10.4153/CMB-2008-062-6
@article{10_4153_CMB_2008_062_6,
author = {Vidanovi\'c, Mirjana V. and Tri\v{c}kovi\'c, Slobodan B. and Stankovi\'c, Miomir S.},
title = {Summation of {Series} over {Bourget} {Functions}},
journal = {Canadian mathematical bulletin},
pages = {627--636},
year = {2008},
volume = {51},
number = {4},
doi = {10.4153/CMB-2008-062-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-062-6/}
}
TY - JOUR AU - Vidanović, Mirjana V. AU - Tričković, Slobodan B. AU - Stanković, Miomir S. TI - Summation of Series over Bourget Functions JO - Canadian mathematical bulletin PY - 2008 SP - 627 EP - 636 VL - 51 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-062-6/ DO - 10.4153/CMB-2008-062-6 ID - 10_4153_CMB_2008_062_6 ER -
%0 Journal Article %A Vidanović, Mirjana V. %A Tričković, Slobodan B. %A Stanković, Miomir S. %T Summation of Series over Bourget Functions %J Canadian mathematical bulletin %D 2008 %P 627-636 %V 51 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2008-062-6/ %R 10.4153/CMB-2008-062-6 %F 10_4153_CMB_2008_062_6
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