Extended Bessel Matrix Functions

This work is devoted to the study of some new families of matrix functions which provide a further extension of the extended Bessel matrix functions. In the sequel, some new and interesting properties of these families of k-Bessel matrix functions have been investigated and the connections between k-Bessel matrix functions and k-Laguerre matrix polynomials are indicated in the concluding section of the paper.

___

  • [1] Çekim, B. and Altin, A.: Matrix analogues of some properties for Bessel functions. Journal of Mathematical Sciences, The University of Tokyo, 22 (2015), no. 2, 519-530.
  • [2] Çekim, B. and Erku¸s-Duman, E.: Integral representations for Bessel matrix functions. Gazi University Journal of Science, 27 (2014), no. 1, 663-667.
  • [3] Dunford, N., and Schwartz, J.T.: Linear Operators, part I, General Theory. Interscience Publishers, INC. New York, 1957.
  • [4] Gorowara, Krishan K., On Bourget’s function Jn,k(z). Ganita, 22 (1971), no. 1, 21-26.
  • [5] Janic, Radovan R., and Mitrovic, Zarko: On generalized Bourget’s function. Publ. Fac. Electrotech. Univ. Belgrade, Ser. Math. Phys. no. 412/460, (1973), 31-35.
  • [6] Jódar, L. Company, R., and Navarro, E.: Solving explicitly the Bessel matrix differential equation, without increasing problem dimension. Congressus Numerantium, 92 (1993), 261-276.
  • [7] Jódar, L. Company, R. and Navarro, E.: Bessel matrix functions: explicit solution of coupled Bessel type equations. Utilitas Mathematica, 46 (1994), 129-141.
  • [8] Jódar, L., and Cortés, J.C.: Some properties of Gamma and Beta matrix functions. Applied Mathematics Letters, 11 (1998), 89-93.
  • [9] Jódar, L., and Cortés, J.C.: On the hypergeometric matrix function. Journal of Computational and Applied Mathematics, 99 (1998), 205-217.
  • [10] Jódar, L., and Cortés, J.C.: Closed form general solution of the hypergeometric matrix differential equation. Mathematical and Computer Modelling, 32 (2000), 1017-1028.
  • [11] Sastre, J., and Jódar, L.: Asymptotics of the modified Bessel and incomplete Gamma matrix functions. Applied Mathematics Letters, 16 (2003), no. 6, 815-820.
  • [12] Shehata, A.: On modified Laguerre matrix polynomials. Journal of Natural Sciences and Mathematics, 8 (2015), no. 2, 153-166.
  • [13] Shehata, A.: Some relations on Laguerre matrix polynomials. Malaysian Journal of Mathematical Sciences, 9 (2015), no. 3, 443-462.
  • [14] Shehata, A.: A new extension of Bessel matrix functions. Southeast Asian Bulletin of Mathematics, 40 (2016), no. 2, 265-288.
  • [15] Shehata, A.: A new kind of Legendre matrix polynomials. Gazi University Journal of Science, 29 (2016), no. 2, 535-558.
  • [16] Shehata, A.: Some relations on Konhauser matrix polynomials. Miskolc Mathematical Notes, 17 (2016), no. 1, 605-633.
  • [17] Shehata, A.: Some properties associated with the Bessel matrix functions. Konuralp Journal of Mathematics (KJM), 5 (2017), no. 2, 24-35.
  • [18] Srivastava, H.M.: A note on a function analogous to Bourget’s function. Ganita, 19 (1968), 45-48.
  • [19] Mubeen, S., Rahman, G., and Arshad, M.: k-gamma, k-beta matrices and their properties. Journal of Mathematical and Computational Science, 5 (2015), 647-657.
  • [20] Mubeen, S., Rahman, G., and Arshad, M.: closed form general solution of the hypergeometric k-matrix differential equation. Journal of Inequalities and Special Functions, 7 (2016), no.1, 39-52.