Geodesic
Some formulas for ordinary and hyper Bessel--Clifford
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 5, pp. 195-208.

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

In this paper, we show that the matrix elements of some Lorentz group representation operators and bases transform operators acting in the representation space, may be expressed in terms of the modified Bessel–Clifford functions and their multi-index analogs introduced by the authors via Delerue hyper Bessel functions. 
@article{FPM_2019_22_5_a19,
     author = {I. Shilin and J. Choi},
     title = {Some formulas for ordinary and hyper {Bessel--Clifford}},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {195--208},
     publisher = {mathdoc},
     volume = {22},
     number = {5},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2019_22_5_a19/}
}
TY  - JOUR
AU  - I. Shilin
AU  - J. Choi
TI  - Some formulas for ordinary and hyper Bessel--Clifford
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2019
SP  - 195
EP  - 208
VL  - 22
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2019_22_5_a19/
LA  - ru
ID  - FPM_2019_22_5_a19
ER  - 
%0 Journal Article
%A I. Shilin
%A J. Choi
%T Some formulas for ordinary and hyper Bessel--Clifford
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2019
%P 195-208
%V 22
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2019_22_5_a19/
%G ru
%F FPM_2019_22_5_a19
I. Shilin; J. Choi. Some formulas for ordinary and hyper Bessel--Clifford. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 5, pp. 195-208. http://geodesic.mathdoc.fr/item/FPM_2019_22_5_a19/

[1] Vilenkin N. Ya., Spetsialnye funktsii i teoriya predstavlenii grupp, Nauka, M., 1991

[2] Vilenkin N. Ya., Shleinikova M. A., “Integralnye sootnosheniya dlya funktsii Uittekera i predstavleniya trekhmernoi gruppy Lorentsa”, Matem. sb., 81:2 (1970), 185–191 | Zbl

[3] Gradshtein I. S., Ryzhik I. M., Tablitsy integralov, summ, ryadov i proizvedenii, Fizmatlit, M., 1963 | MR

[4] Klyuchantsev M. I., “Singulyarnye differentsialnye operatory s $r-1$ parametrami i funktsii Besselya vektornogo indeksa”, Sib. matem. zhurn., 24:3 (1983), 47–62 | MR | Zbl

[5] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady, v. 1, Elementarnye funktsii, Nauka, M., 1981 | MR

[6] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady, v. 2, Spetsialnye funktsii, Nauka, M., 1981 | MR

[7] Abramowitz M., “Coulomb wave functions expressed in terms of Bessel–Clifford functions”, J. Math. Phys., 33 (1954), 111–116 | DOI | MR | Zbl

[8] Chaggara H., Ben Romdhane N., “On the zeros of the hyper-Bessel function”, Integral Transform. Spec. Funct., 26:2 (2015), 96–101 | DOI | MR | Zbl

[9] Chaudhry M. A., Zubair S. M., “Extended incomplete gamma functions with applications”, J. Math. Anal. Appl., 274:2 (2002), 725–745 | DOI | MR | Zbl

[10] Choi J., Shilin I. A., “A family of series and integrals involving Whittaker, Bessel functions, and their products derivable from the representation of the group $\mathrm{SO}(2,1)$”, Commun. Korean Math. Soc., 32:4 (2017), 999–1008 | MR | Zbl

[11] Clifford W. K., “On Bessel's functions”, Mathematical Papers, Oxford Univ. Press, London, 1882, 346–349

[12] Dattoli G., Maino G, Chicco C., Lorenzutta S., Torre A., “A unified point of view on the theory of generalized Bessel functions”, Comput. Math. Appl., 30:7 (1995), 113–125 | DOI | MR | Zbl

[13] Delerue P., “Sur le calcul symbolique à $n$ variables et les fonctions hyperbesseliennes”, Ann. Soc. Sci. Bruxelles, 67:3 (1953), 229–274 | MR | Zbl

[14] Erdélyi A., Magnus W., Oberhettinger F., Tricomi F. G., Higher Transcendental Functions, v. II, McGraw-Hill, New York, 1953 | MR

[15] Erdélyi A., Magnus W., Oberhettinger F., Tricomi F. G., Tables of Integral Transforms, v. I, McGraw-Hill, New York, 1954 | MR

[16] Erdélyi A., Magnus W., Oberhettinger F., Tricomi F. G., Tables of Integral Transforms, v. II, McGraw-Hill, New York, 1954 | MR

[17] Gorenflo R., Kilbas A., Mainardi F., Rogosin S., Mittag-Leffler Functions, Related Topics and Applications, Springer, Berlin, 2014 | MR | Zbl

[18] Hayek N., Pérez-Acosta F., “Asymptotic expressions of the Dirac delta function in terms of the Bessel–Clifford functions”, Pure Appl. Math. Sci., 37 (1993), 53–56 | MR | Zbl

[19] Kiryakova V., “Transmutation method for solving hyper-Bessel differential equations based on the Poisson–Dimovsky transformation”, Frac. Calc. Appl. Anal., 11:3 (2008), 299–316 | MR | Zbl

[20] Kiryakova V., “The special functions of fractional calculus as generalized fractional calculus operators of some basic functions”, Comput. Math. Appl., 59:3 (2010), 1128–1141 | DOI | MR | Zbl

[21] Klauder J. R., Penson K. A., Sixdeniers J.-M., “Constructing coherent states through solutions of Stieltjes and Hausdorff moment problems”, Phys. Rev. A, 64 (2001), 013817 | DOI

[22] Paneva-Konovska J., “A family of hyper-Bessel functions and convergent series in them”, Frac. Calc. Appl. Anal., 17:4 (2014), 1001–1015 | MR | Zbl

[23] Rainville E. D., Special Functions, Macmillan, New York, 1960 | MR | Zbl

[24] Shilin I. A., Choi J., “Certain connections between the spherical and hyperbolic bases on the cone and formulas for related special functions”, Integral Transform. Spec. Funct., 25:5 (2014), 374–383 | DOI | MR | Zbl

[25] Shilin I. A., Choi J., “Certain relations between Bessel and Whittaker functions related to some diagonal and block-diagonal $3\times3$-matrices”, J. Nonlinear Sci. Appl., 10:2 (2017), 560–574 | DOI | MR | Zbl

[26] Srivastava H. M., Getinkaya A., Kiymaz O., “A certain generalized Pochhammer symbol and its applications to hypergeometric functions”, Appl. Math. Comput., 226:1 (2014), 484–491 | MR | Zbl

[27] Srivastava H. M., Manocha H. L., A Treatise on Generating Functions, Halsted Press, New York, 1984 | MR | Zbl

[28] Witte N. S., “Exact solution for the reflection and diffraction of atomic de Broglie waves by a travelling evanescent laser wave”, J. Phys. A: Math. Gen., 31 (1998), 807 | DOI | Zbl

[29] Yasar B. Y., Özarslan M. A., “Unified Bessel, modified Bessel, spherical Bessel and Bessel–Clifford functions”, J. Ineq. Spec. Func., 7:4 (2016), 77–117 | MR