The main aim of this work is the development of some interesting properties which are associated with the Bessel matrix functions and its relationship with the hypergeometric matrix functions.
[1] Al-Salam, W.A. and Carlitz, L.: Some functions associated with the Bessel functions. J. Math. Mech., Vol. 12 (1963), 911-933.
[2] Bateman, H. and Rice, S.O.: Some expansion associated with Bessel functions. Proc Natl Acad Sci USA, Vol. 21, No. 3 (1935), 173-179.
[3] C ekim, B. and Altin, A.: Matrix analogues of some properties for Bessel matrix functions. J. Math. Sci. Univ. Tokyo, Vol. 22, No. 2 (2015), 519-530.
[4] C ekim, B. and Erkus-Duman, E.: Integral representations for Bessel matrix functions. Gazi Univ. J. Sci., Vol. 27, No. 1 (2014), 663-667.
[5] Chatterjea, S.K.: On a function with the Bessel functions. Ann. Univ. Ferrara Sez. VII Sci. Mat., Vol. 10, No. 1 (1961), 13-16.
[6] Defez, E., and Jodar, L.: Some applications of the Hermite matrix polynomials series expansions. J. Comput. Appl. Math.. Vol. 99 (1998), 105-117.
[7] Dunford, N., and Schwartz, J.T.: Linear Operators, part I, General Theory. Interscience Publishers, INC. New York, 1957.
[8] Defez, E., and Jodar, L. Chebyshev matrix polynomials and second order matrix differential equations. Util. Math., Vol. 61 (2002), 107-123.
[9] Jodar, L. Company, R., and Navarro, E.: Solving explicitly the Bessel matrix differential equation, without increasing problem dimension. Congr. Numer., Vol. 92 (1993), 261-276.
[10] Jodar, L. Company, R. and Navarro, E.: Bessel matrix functions: explicit solution of coupled Bessel type equations. Util. Math., Vol. 46 (1994), 129-141.
[11] Jodar, L., and Cortes, J.C.: Some properties of Gamma and Beta matrix functions. Appl. Math. Lett., Vol. 11, (1998), 89-93.
[12] Jodar, L., and Cortes, J.C.: On the hypergeometric matrix function. J. Comput. Appl. Math., Vol. 99 (1998), 205-217.
[13] Jodar, L., and Cortes, J.C.: Closed form general solution of the hypergeometric matrix dierential equation. Math. Comput. Model., Vol. 32 (2000), 1017-1028.
[14] Sastre, J., and Jodar, L.: Asymptotics of the modied Bessel and incomplete Gamma matrix functions. Appl. Math. Lett., Vol. 16, No. 6 (2003), 815-820.
[15] Shehata, A.: On modied Laguerre matrix polynomials. J. Nat. Sci. Math., Vol. 8, No. 2 (2015), 153-166.
[16] Shehata, A.: Some relations on Laguerre matrix polynomials. Malays. J. Math. Sci., Vol. 9, No. 3 (2015), 443-462.
[17] Shehata, A.: A new extension of Bessel matrix functions. Southeast Asian Bull. Math., Vol. 40, No. 2 (2016), 265-288.
[18] Shehata, A.: A new kind of Legendre matrix polynomials. Gazi Univ. J. Sci., Vol. 29, No. 2 (2016), 535-558.
[19] Shehata, A.: Some relations on Konhauser matrix polynomials. Miskolc Math. Notes, Vol. 17, No. 1 (2016), 605-633.
[20] Srivastava, H.M.: An entire function associated with the Bessel functions. Collect. Math., Vol. 16 (1964), 127-148.
Year 2017,
Volume: 5 Issue: 2, 24 - 35, 15.10.2017
[1] Al-Salam, W.A. and Carlitz, L.: Some functions associated with the Bessel functions. J. Math. Mech., Vol. 12 (1963), 911-933.
[2] Bateman, H. and Rice, S.O.: Some expansion associated with Bessel functions. Proc Natl Acad Sci USA, Vol. 21, No. 3 (1935), 173-179.
[3] C ekim, B. and Altin, A.: Matrix analogues of some properties for Bessel matrix functions. J. Math. Sci. Univ. Tokyo, Vol. 22, No. 2 (2015), 519-530.
[4] C ekim, B. and Erkus-Duman, E.: Integral representations for Bessel matrix functions. Gazi Univ. J. Sci., Vol. 27, No. 1 (2014), 663-667.
[5] Chatterjea, S.K.: On a function with the Bessel functions. Ann. Univ. Ferrara Sez. VII Sci. Mat., Vol. 10, No. 1 (1961), 13-16.
[6] Defez, E., and Jodar, L.: Some applications of the Hermite matrix polynomials series expansions. J. Comput. Appl. Math.. Vol. 99 (1998), 105-117.
[7] Dunford, N., and Schwartz, J.T.: Linear Operators, part I, General Theory. Interscience Publishers, INC. New York, 1957.
[8] Defez, E., and Jodar, L. Chebyshev matrix polynomials and second order matrix differential equations. Util. Math., Vol. 61 (2002), 107-123.
[9] Jodar, L. Company, R., and Navarro, E.: Solving explicitly the Bessel matrix differential equation, without increasing problem dimension. Congr. Numer., Vol. 92 (1993), 261-276.
[10] Jodar, L. Company, R. and Navarro, E.: Bessel matrix functions: explicit solution of coupled Bessel type equations. Util. Math., Vol. 46 (1994), 129-141.
[11] Jodar, L., and Cortes, J.C.: Some properties of Gamma and Beta matrix functions. Appl. Math. Lett., Vol. 11, (1998), 89-93.
[12] Jodar, L., and Cortes, J.C.: On the hypergeometric matrix function. J. Comput. Appl. Math., Vol. 99 (1998), 205-217.
[13] Jodar, L., and Cortes, J.C.: Closed form general solution of the hypergeometric matrix dierential equation. Math. Comput. Model., Vol. 32 (2000), 1017-1028.
[14] Sastre, J., and Jodar, L.: Asymptotics of the modied Bessel and incomplete Gamma matrix functions. Appl. Math. Lett., Vol. 16, No. 6 (2003), 815-820.
[15] Shehata, A.: On modied Laguerre matrix polynomials. J. Nat. Sci. Math., Vol. 8, No. 2 (2015), 153-166.
[16] Shehata, A.: Some relations on Laguerre matrix polynomials. Malays. J. Math. Sci., Vol. 9, No. 3 (2015), 443-462.
[17] Shehata, A.: A new extension of Bessel matrix functions. Southeast Asian Bull. Math., Vol. 40, No. 2 (2016), 265-288.
[18] Shehata, A.: A new kind of Legendre matrix polynomials. Gazi Univ. J. Sci., Vol. 29, No. 2 (2016), 535-558.
[19] Shehata, A.: Some relations on Konhauser matrix polynomials. Miskolc Math. Notes, Vol. 17, No. 1 (2016), 605-633.
[20] Srivastava, H.M.: An entire function associated with the Bessel functions. Collect. Math., Vol. 16 (1964), 127-148.