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On The Konhauser Biorthogonal Polynomials

Year 2017, Volume: 7, 48 - 55, 19.12.2017

Abstract

In this study, we give new properties of the Konhauser biorthogonal polynomials $Y_{n}^{\alpha }(x;k)$. Various families of multilinear, multilateral generating functions, some special cases and several recurrence relations for these polynomials are obtained.

References

  • Aktaş, R., Erkuş-Duman, E., The Laguerre polynomials in several variables, Mathematica Slovaca, 63(3)(2013), 531–544.
  • Aktaş, R., Erkus-Duman, E., A generalization of the extended Jacobi polynomials in two variables, Gazi University Journal of Science, 28(3)(2015), 503–521.
  • Aktaş, R., Taşdelen, F., Yavuz, N. , Bilateral and bilinear generating functions for the eneralized Zernike or disc polynomials, Ars Combinatoria, 108(2013), 389–400.
  • Altın A., Erkuş, E. On a multivariable extension of the Lagrange-Hermite polynomials, Integral Transforms and Special Functions, 17(4)(2006), 239–244.
  • Erdelyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G., Higher Transcendental Functions, Vol. III, McGraw–Hill Book Company, New York/Toronto/London, 1955.
  • Erkus, E., Srivastava, H. M., A unified presentation of some families of multivariable polynomials, Integral Transforms Spec. Funct., 17(2006), 267–273.
  • Gürel, Ö., Aktaş, R., Altın, A., On a family of multivariable polynomials defined through Rodrigues type formula, Journal of Classical Analysis, 4(2)(2014), 167–180.
  • Özmen, N., Erkus-Duman, E., Some results for a family of multivariable polynomials, AIP Conf. Proc., 1558(2013), 1124–1127.
  • Özmen, N., Erkus-Duman, E., On the Poisson-Charlier polynomials, Serdica Math. J., 41(2015), 457–470.
  • Özmen, N., Erkuş-Duman, E., Some families of generating functions for the generalized Cesa´ro polynomials, J. Comput. Anal. Appl., 25(4)(2018), 670–683.
  • Srivastava, H. M., Manocha, H. L., A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, 1984.
  • Srivastava, H. M., Taşdelen, F., Şekeroğlu, B., Some families of generating functions for the q-Konhauser polynomials, Taiwanese J. Math., 12(3)(2008), 841–850.
  • Şekeroğlu, B., Srivastava H.M., Taşdelen, F., Some properties of q-biorthogonal polynomials, J. Math. Anal. Appl., 326(2)(2007), 896–907.
  • Taşdelen, F., Çekim, B., Aktaş, R., On a multivariable extension of Jacobi matrix polynomials, Computers and Mathematics with Applications, 61(2011), 2412–2423.
  • Varma, S., Tasdelen F., Biorthogonal matrix polynomials related to Jacobi matrix polynomials, Computers & Mathematics with Applications,62(2011), 3663-3668.
Year 2017, Volume: 7, 48 - 55, 19.12.2017

Abstract

References

  • Aktaş, R., Erkuş-Duman, E., The Laguerre polynomials in several variables, Mathematica Slovaca, 63(3)(2013), 531–544.
  • Aktaş, R., Erkus-Duman, E., A generalization of the extended Jacobi polynomials in two variables, Gazi University Journal of Science, 28(3)(2015), 503–521.
  • Aktaş, R., Taşdelen, F., Yavuz, N. , Bilateral and bilinear generating functions for the eneralized Zernike or disc polynomials, Ars Combinatoria, 108(2013), 389–400.
  • Altın A., Erkuş, E. On a multivariable extension of the Lagrange-Hermite polynomials, Integral Transforms and Special Functions, 17(4)(2006), 239–244.
  • Erdelyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G., Higher Transcendental Functions, Vol. III, McGraw–Hill Book Company, New York/Toronto/London, 1955.
  • Erkus, E., Srivastava, H. M., A unified presentation of some families of multivariable polynomials, Integral Transforms Spec. Funct., 17(2006), 267–273.
  • Gürel, Ö., Aktaş, R., Altın, A., On a family of multivariable polynomials defined through Rodrigues type formula, Journal of Classical Analysis, 4(2)(2014), 167–180.
  • Özmen, N., Erkus-Duman, E., Some results for a family of multivariable polynomials, AIP Conf. Proc., 1558(2013), 1124–1127.
  • Özmen, N., Erkus-Duman, E., On the Poisson-Charlier polynomials, Serdica Math. J., 41(2015), 457–470.
  • Özmen, N., Erkuş-Duman, E., Some families of generating functions for the generalized Cesa´ro polynomials, J. Comput. Anal. Appl., 25(4)(2018), 670–683.
  • Srivastava, H. M., Manocha, H. L., A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, 1984.
  • Srivastava, H. M., Taşdelen, F., Şekeroğlu, B., Some families of generating functions for the q-Konhauser polynomials, Taiwanese J. Math., 12(3)(2008), 841–850.
  • Şekeroğlu, B., Srivastava H.M., Taşdelen, F., Some properties of q-biorthogonal polynomials, J. Math. Anal. Appl., 326(2)(2007), 896–907.
  • Taşdelen, F., Çekim, B., Aktaş, R., On a multivariable extension of Jacobi matrix polynomials, Computers and Mathematics with Applications, 61(2011), 2412–2423.
  • Varma, S., Tasdelen F., Biorthogonal matrix polynomials related to Jacobi matrix polynomials, Computers & Mathematics with Applications,62(2011), 3663-3668.
There are 15 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Nejla Özmen

Yahya Cin

Publication Date December 19, 2017
Published in Issue Year 2017 Volume: 7

Cite

APA Özmen, N., & Cin, Y. (2017). On The Konhauser Biorthogonal Polynomials. Turkish Journal of Mathematics and Computer Science, 7, 48-55.
AMA Özmen N, Cin Y. On The Konhauser Biorthogonal Polynomials. TJMCS. December 2017;7:48-55.
Chicago Özmen, Nejla, and Yahya Cin. “On The Konhauser Biorthogonal Polynomials”. Turkish Journal of Mathematics and Computer Science 7, December (December 2017): 48-55.
EndNote Özmen N, Cin Y (December 1, 2017) On The Konhauser Biorthogonal Polynomials. Turkish Journal of Mathematics and Computer Science 7 48–55.
IEEE N. Özmen and Y. Cin, “On The Konhauser Biorthogonal Polynomials”, TJMCS, vol. 7, pp. 48–55, 2017.
ISNAD Özmen, Nejla - Cin, Yahya. “On The Konhauser Biorthogonal Polynomials”. Turkish Journal of Mathematics and Computer Science 7 (December 2017), 48-55.
JAMA Özmen N, Cin Y. On The Konhauser Biorthogonal Polynomials. TJMCS. 2017;7:48–55.
MLA Özmen, Nejla and Yahya Cin. “On The Konhauser Biorthogonal Polynomials”. Turkish Journal of Mathematics and Computer Science, vol. 7, 2017, pp. 48-55.
Vancouver Özmen N, Cin Y. On The Konhauser Biorthogonal Polynomials. TJMCS. 2017;7:48-55.