Geodesic
New classes of generating functions for generalized Bessel functions with satisfy the ordinary differential equation of the $m$-order
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 561-567.

Voir la notice de l'article provenant de la source Math-Net.Ru

For generalized Bessel functions which satisfy the ordinary differential equation of the $m$-order of special type new classes of generating functions (associated with Stirling numbers of the second kind) are derived. Relevant connections of this new formulas with those given in earlier works on the subject are also indicated.
Keywords: generalized Bessel functions, generating functions, Stirling numbers. 
@article{SEMR_2012_9_a35,
     author = {M. D. Khriptun},
     title = {New classes of generating functions for generalized {Bessel} functions with satisfy the ordinary differential equation of the $m$-order},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {561--567},
     publisher = {mathdoc},
     volume = {9},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2012_9_a35/}
}
TY  - JOUR
AU  - M. D. Khriptun
TI  - New classes of generating functions for generalized Bessel functions with satisfy the ordinary differential equation of the $m$-order
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2012
SP  - 561
EP  - 567
VL  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2012_9_a35/
LA  - ru
ID  - SEMR_2012_9_a35
ER  - 
%0 Journal Article
%A M. D. Khriptun
%T New classes of generating functions for generalized Bessel functions with satisfy the ordinary differential equation of the $m$-order
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2012
%P 561-567
%V 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2012_9_a35/
%G ru
%F SEMR_2012_9_a35
M. D. Khriptun. New classes of generating functions for generalized Bessel functions with satisfy the ordinary differential equation of the $m$-order. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 9 (2012), pp. 561-567. http://geodesic.mathdoc.fr/item/SEMR_2012_9_a35/

[1] Mathai A. M., Saxena R. K., Generalized hypergeometric functions with applications in statistics and physical sciences, Springer-Verlag, Berlin–Heidelberg–New-York, 1973 | MR

[2] Srivastava H. M., Kashyap B. R. K., Special functions in Queueing Theory and related Stochastic processes, Academic Press, New-York, 1982 | MR

[3] Riordan J., Combinatorial Identities, Wiley Tracts of Probability and Statistics, John Wiley and Sons, New-York–London–Sydney, 1968 | MR | Zbl

[4] Singhal J. P., Srivastava H. M., “A class of bilateral generating functions for certain classical polynomials”, Pacific J. Math., 42 (1972), 755–762 | DOI | MR

[5] Srivastava H. M., “Some families of generating functions associated with the Stirling numbers of the second kind”, J. Math Anal. Appl., 251 (2000), 752–769 | DOI | MR | Zbl

[6] Khriptun M. D., “Teoremy umnozheniya dlya reshenii obobschennogo differentsialnogo uravneniya Besselya $m$-go poryadka”, Dif. uravneniya, 11:2 (1975), 287–293 | Zbl

[7] Luchak G., “The solution of the single-channel queueing equations characterized by a time-dependent Poisson distributed arrival rate and general class of holding times”, Oper. Res., 4 (1956), 711–732 | DOI | MR

[8] Luchak G., “The distribution of the time required to reduce to some preassigned level a simple channel queue characterized by a time dependent Poisson-distributed arrival rate and a general class of holding times”, Operations Research, 5 (1957), 205–209 | DOI | MR

[9] Luchak G., “The continuous time solution of the equations of the simple channel queue with a general class of service-time distributions by the method of generating functions”, Journal Roy. Statist. Soc. B, 20 (1958), 176–181 | MR | Zbl

[10] Watson G. N., A Treatise of the Theory of Bessel Functions, Second Edition, Cambridge Univ. Press, Cambridge– London–New-York, 1944 | MR | Zbl