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SOME PROPERTIES ASSOCIATED WITH THE BESSEL MATRIX FUNCTIONS

Year 2017, Volume: 5 Issue: 2, 24 - 35, 15.10.2017

Abstract

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.

References

  • [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 di erential equation. Math. Comput. Model., Vol. 32 (2000), 1017-1028.
  • [14] Sastre, J., and Jodar, L.: Asymptotics of the modi ed Bessel and incomplete Gamma matrix functions. Appl. Math. Lett., Vol. 16, No. 6 (2003), 815-820.
  • [15] Shehata, A.: On modi ed 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

Abstract

References

  • [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 di erential equation. Math. Comput. Model., Vol. 32 (2000), 1017-1028.
  • [14] Sastre, J., and Jodar, L.: Asymptotics of the modi ed Bessel and incomplete Gamma matrix functions. Appl. Math. Lett., Vol. 16, No. 6 (2003), 815-820.
  • [15] Shehata, A.: On modi ed 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.
There are 18 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Ayman Shehata

Publication Date October 15, 2017
Submission Date October 13, 2017
Acceptance Date February 7, 2017
Published in Issue Year 2017 Volume: 5 Issue: 2

Cite

APA Shehata, A. (2017). SOME PROPERTIES ASSOCIATED WITH THE BESSEL MATRIX FUNCTIONS. Konuralp Journal of Mathematics, 5(2), 24-35.
AMA Shehata A. SOME PROPERTIES ASSOCIATED WITH THE BESSEL MATRIX FUNCTIONS. Konuralp J. Math. October 2017;5(2):24-35.
Chicago Shehata, Ayman. “SOME PROPERTIES ASSOCIATED WITH THE BESSEL MATRIX FUNCTIONS”. Konuralp Journal of Mathematics 5, no. 2 (October 2017): 24-35.
EndNote Shehata A (October 1, 2017) SOME PROPERTIES ASSOCIATED WITH THE BESSEL MATRIX FUNCTIONS. Konuralp Journal of Mathematics 5 2 24–35.
IEEE A. Shehata, “SOME PROPERTIES ASSOCIATED WITH THE BESSEL MATRIX FUNCTIONS”, Konuralp J. Math., vol. 5, no. 2, pp. 24–35, 2017.
ISNAD Shehata, Ayman. “SOME PROPERTIES ASSOCIATED WITH THE BESSEL MATRIX FUNCTIONS”. Konuralp Journal of Mathematics 5/2 (October 2017), 24-35.
JAMA Shehata A. SOME PROPERTIES ASSOCIATED WITH THE BESSEL MATRIX FUNCTIONS. Konuralp J. Math. 2017;5:24–35.
MLA Shehata, Ayman. “SOME PROPERTIES ASSOCIATED WITH THE BESSEL MATRIX FUNCTIONS”. Konuralp Journal of Mathematics, vol. 5, no. 2, 2017, pp. 24-35.
Vancouver Shehata A. SOME PROPERTIES ASSOCIATED WITH THE BESSEL MATRIX FUNCTIONS. Konuralp J. Math. 2017;5(2):24-35.
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