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Year 2018, , 1 - 11, 27.04.2018
https://doi.org/10.36753/mathenot.421743

Abstract

References

  • [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.

Extended Bessel Matrix Functions

Year 2018, , 1 - 11, 27.04.2018
https://doi.org/10.36753/mathenot.421743

Abstract

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.

References

  • [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.
There are 20 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Ayman Shehata

Publication Date April 27, 2018
Submission Date May 30, 2017
Published in Issue Year 2018

Cite

APA Shehata, A. (2018). Extended Bessel Matrix Functions. Mathematical Sciences and Applications E-Notes, 6(1), 1-11. https://doi.org/10.36753/mathenot.421743
AMA Shehata A. Extended Bessel Matrix Functions. Math. Sci. Appl. E-Notes. April 2018;6(1):1-11. doi:10.36753/mathenot.421743
Chicago Shehata, Ayman. “Extended Bessel Matrix Functions”. Mathematical Sciences and Applications E-Notes 6, no. 1 (April 2018): 1-11. https://doi.org/10.36753/mathenot.421743.
EndNote Shehata A (April 1, 2018) Extended Bessel Matrix Functions. Mathematical Sciences and Applications E-Notes 6 1 1–11.
IEEE A. Shehata, “Extended Bessel Matrix Functions”, Math. Sci. Appl. E-Notes, vol. 6, no. 1, pp. 1–11, 2018, doi: 10.36753/mathenot.421743.
ISNAD Shehata, Ayman. “Extended Bessel Matrix Functions”. Mathematical Sciences and Applications E-Notes 6/1 (April 2018), 1-11. https://doi.org/10.36753/mathenot.421743.
JAMA Shehata A. Extended Bessel Matrix Functions. Math. Sci. Appl. E-Notes. 2018;6:1–11.
MLA Shehata, Ayman. “Extended Bessel Matrix Functions”. Mathematical Sciences and Applications E-Notes, vol. 6, no. 1, 2018, pp. 1-11, doi:10.36753/mathenot.421743.
Vancouver Shehata A. Extended Bessel Matrix Functions. Math. Sci. Appl. E-Notes. 2018;6(1):1-11.

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