Research Article
BibTex RIS Cite

Some new properties of the Meixner polynomials

Year 2017, Volume: 21 Issue: 6, 1454 - 1462, 01.12.2017
https://doi.org/10.16984/saufenbilder.331327

Abstract

The present study deals with some new properties for the
Meixner polynomials. In this manuscript we obtain a number of families of bilineer
and bilateral generating functions, general properties and also some special
cases for these polynomials. In addition, we derive a theorem giving certain
families of bilateral generating functions for the generalized Lauricella functions
and the Meixner polynomials. Finally, we get several interesting results of
this theorem.

References

  • H. M., Srivastava, and H. L. A. , Manocha, ‘‘Treatise on Generating Functions’’, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, 1984.
  • D. V. Kruchinin and V. V. Kruchinin, ‘‘Explicit Formulas for Meixner Polynomials’’, Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 2015.
  • H. M., Srivastava, and M.C. , Daoust, ‘‘Certain generalized Neumann expansions associated with the Kampé de Fériet function’’, Nederl. akad. Westensch. Indag. Math. 31, pp. 449-457, 1969.
  • S-J., Liu, S-D., Lin, H.M., Srivastava, M-M., Wong, ‘‘Bilateral generating functions for the Erkus-Srivastava polynomials and the generalized Lauricella functions’’, Applied Mathematics and Computation 218, 7685–7693, 2012.
  • N., Özmen and E., Erkuş-Duman, ‘‘Some families of generating functions for the generalized Cesáro polynomials’’, J. Comput. Anal. Appl., J. Computational Analysis and Applications, Vol. 25, No.4, Copyright 2018 Eudoxus Press,LLC, 670-683, 2018.
  • G., Lauricella,‘‘Sulle funzioni ipergeometriche a più variabili’’, Rend. Circ. Mat. Palermo 7, 111-158, 1893.
  • H. , Exton, ‘‘Multiple Hypergeometric Functions and Applicaions’’, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1976.
  • M.I. , Qureshi, M.S. , Khan and M.A. , Pathan, ‘‘Some multiple Gaussian hypergeometric generalizations of Buschman--Srivastava theorem’’, Internal J. Math. Math. Sci. 2005, 143-153, 2005.
  • H.M., Srivastava, and P.W., Karlsson, ‘‘Multiple Gaussian Hypergeometric Series’’, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985.
  • N. , Özmen, and E. , Erkuş-Duman, ‘‘On the Poisson-Charlier polynomials’’, Serdica Math. J. 41. 457-470, 2015.
  • H. M. Srivastava, M. A. Özarslan and C. Kaanoğlu, ‘‘Some families of generating functions for a certain class of three-variable polynomials’’, Integral Transforms and Special Functions, Vol. 21, No. 12, 885-896, 2010.
  • E., Erkuş and H.M., Srivastava, ‘‘A unified presentation of some families of multivariable polynomials, Integral Transforms Spec. Funct. 17, pp. 267–273, 2006.
  • S.-D. , Lin, H.M. , Srivastava and P.-Y., Wang, ‘‘Some families of hypergeometric transformations and generating relations’’, Math. Comput. Modelling 36, pp. 445–459, 2002.
  • S.-J., Liu, ‘‘Bilateral generating functions for the Lagrange polynomials and the Lauricella functions’’, Integral Transforms Spec. Funct. 20, pp. 519–527, 2009.
  • M. A., Özarslan and A., Altın, ‘‘ Some Families of generating functions for the multiple orthogonal polynomials associated with modified Bessel K-functions’’, J. Math. Anal. Appl. 297, pp. 186–193, 2004.
  • E., Özergin, M.A., Özarslan and H.M., Srivastava, ‘‘Some families of generating functions for a class of bivariate polynomials’’, Math. Comput. Modelling 50, pp. 1113–1120, 2009.
  • V.K., Dmitry and V., Yuriy, ‘‘Explicit Formulas for Meixner Polynomials’’, Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 2015. (Article ID 620569, 5 pages DOI: 10.1155/2015/620569).
  • A., Jooste, K., Jordaan and F. Toókos, ‘‘On the zeros of Meixner polynomials’’, Numer. Math. Volume 124, pp. 57–71, 2013.
  • R. , Aktaş and E., Erkuş-Duman, ‘‘The Laguerre polynomials in several variables’’, Mathematica Slovaca, 63(3), 531-544, 2013.
  • S-J., Liu, C-J., Chyan, H-C., Lu and H.M., Srivastava, ‘‘Bilateral generating functions for the Chan–Chyan–Srivastava polynomials and the generalized Lauricella functions’’, Integral Transforms and Special Functions Vol. 23, No. 7, 539–549, 2012.
  • F., Taşdelen, Ç. Bayram and A., Rabia, ‘‘On a multivariable extension of Jacobi matrix polynomials’’, Computers and Mathematics with Applications 61, 2412–2423, 2011.

Meixner polinomlarının bazı yeni özellikleri

Year 2017, Volume: 21 Issue: 6, 1454 - 1462, 01.12.2017
https://doi.org/10.16984/saufenbilder.331327

Abstract

Bu çalışma Meixner polinomlar için bazı yeni özellikler ele
alınmıştır. Burada elde edilen sonuçlar Meixner polinomların bilineer ve bilateral
doğurucu fonksiyonların çeşitli ailelerini, çeşitli özelliklerini ve bazı özel
durumlarını içermektedir. Bunlara ek olarak genelleştirilmiş Lauricella
fonksiyonları  ve Meixner polinomları için
bilateral doğurucu fonksiyon içeren teorem verildi. Son olarak, bu teoremin
ilginç bazı sonuçları verildi.

References

  • H. M., Srivastava, and H. L. A. , Manocha, ‘‘Treatise on Generating Functions’’, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, 1984.
  • D. V. Kruchinin and V. V. Kruchinin, ‘‘Explicit Formulas for Meixner Polynomials’’, Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 2015.
  • H. M., Srivastava, and M.C. , Daoust, ‘‘Certain generalized Neumann expansions associated with the Kampé de Fériet function’’, Nederl. akad. Westensch. Indag. Math. 31, pp. 449-457, 1969.
  • S-J., Liu, S-D., Lin, H.M., Srivastava, M-M., Wong, ‘‘Bilateral generating functions for the Erkus-Srivastava polynomials and the generalized Lauricella functions’’, Applied Mathematics and Computation 218, 7685–7693, 2012.
  • N., Özmen and E., Erkuş-Duman, ‘‘Some families of generating functions for the generalized Cesáro polynomials’’, J. Comput. Anal. Appl., J. Computational Analysis and Applications, Vol. 25, No.4, Copyright 2018 Eudoxus Press,LLC, 670-683, 2018.
  • G., Lauricella,‘‘Sulle funzioni ipergeometriche a più variabili’’, Rend. Circ. Mat. Palermo 7, 111-158, 1893.
  • H. , Exton, ‘‘Multiple Hypergeometric Functions and Applicaions’’, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1976.
  • M.I. , Qureshi, M.S. , Khan and M.A. , Pathan, ‘‘Some multiple Gaussian hypergeometric generalizations of Buschman--Srivastava theorem’’, Internal J. Math. Math. Sci. 2005, 143-153, 2005.
  • H.M., Srivastava, and P.W., Karlsson, ‘‘Multiple Gaussian Hypergeometric Series’’, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1985.
  • N. , Özmen, and E. , Erkuş-Duman, ‘‘On the Poisson-Charlier polynomials’’, Serdica Math. J. 41. 457-470, 2015.
  • H. M. Srivastava, M. A. Özarslan and C. Kaanoğlu, ‘‘Some families of generating functions for a certain class of three-variable polynomials’’, Integral Transforms and Special Functions, Vol. 21, No. 12, 885-896, 2010.
  • E., Erkuş and H.M., Srivastava, ‘‘A unified presentation of some families of multivariable polynomials, Integral Transforms Spec. Funct. 17, pp. 267–273, 2006.
  • S.-D. , Lin, H.M. , Srivastava and P.-Y., Wang, ‘‘Some families of hypergeometric transformations and generating relations’’, Math. Comput. Modelling 36, pp. 445–459, 2002.
  • S.-J., Liu, ‘‘Bilateral generating functions for the Lagrange polynomials and the Lauricella functions’’, Integral Transforms Spec. Funct. 20, pp. 519–527, 2009.
  • M. A., Özarslan and A., Altın, ‘‘ Some Families of generating functions for the multiple orthogonal polynomials associated with modified Bessel K-functions’’, J. Math. Anal. Appl. 297, pp. 186–193, 2004.
  • E., Özergin, M.A., Özarslan and H.M., Srivastava, ‘‘Some families of generating functions for a class of bivariate polynomials’’, Math. Comput. Modelling 50, pp. 1113–1120, 2009.
  • V.K., Dmitry and V., Yuriy, ‘‘Explicit Formulas for Meixner Polynomials’’, Hindawi Publishing Corporation International Journal of Mathematics and Mathematical Sciences Volume 2015. (Article ID 620569, 5 pages DOI: 10.1155/2015/620569).
  • A., Jooste, K., Jordaan and F. Toókos, ‘‘On the zeros of Meixner polynomials’’, Numer. Math. Volume 124, pp. 57–71, 2013.
  • R. , Aktaş and E., Erkuş-Duman, ‘‘The Laguerre polynomials in several variables’’, Mathematica Slovaca, 63(3), 531-544, 2013.
  • S-J., Liu, C-J., Chyan, H-C., Lu and H.M., Srivastava, ‘‘Bilateral generating functions for the Chan–Chyan–Srivastava polynomials and the generalized Lauricella functions’’, Integral Transforms and Special Functions Vol. 23, No. 7, 539–549, 2012.
  • F., Taşdelen, Ç. Bayram and A., Rabia, ‘‘On a multivariable extension of Jacobi matrix polynomials’’, Computers and Mathematics with Applications 61, 2412–2423, 2011.
There are 21 citations in total.

Details

Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Nejla Özmen

Publication Date December 1, 2017
Submission Date July 27, 2017
Acceptance Date September 21, 2017
Published in Issue Year 2017 Volume: 21 Issue: 6

Cite

APA Özmen, N. (2017). Some new properties of the Meixner polynomials. Sakarya University Journal of Science, 21(6), 1454-1462. https://doi.org/10.16984/saufenbilder.331327
AMA Özmen N. Some new properties of the Meixner polynomials. SAUJS. December 2017;21(6):1454-1462. doi:10.16984/saufenbilder.331327
Chicago Özmen, Nejla. “Some New Properties of the Meixner Polynomials”. Sakarya University Journal of Science 21, no. 6 (December 2017): 1454-62. https://doi.org/10.16984/saufenbilder.331327.
EndNote Özmen N (December 1, 2017) Some new properties of the Meixner polynomials. Sakarya University Journal of Science 21 6 1454–1462.
IEEE N. Özmen, “Some new properties of the Meixner polynomials”, SAUJS, vol. 21, no. 6, pp. 1454–1462, 2017, doi: 10.16984/saufenbilder.331327.
ISNAD Özmen, Nejla. “Some New Properties of the Meixner Polynomials”. Sakarya University Journal of Science 21/6 (December 2017), 1454-1462. https://doi.org/10.16984/saufenbilder.331327.
JAMA Özmen N. Some new properties of the Meixner polynomials. SAUJS. 2017;21:1454–1462.
MLA Özmen, Nejla. “Some New Properties of the Meixner Polynomials”. Sakarya University Journal of Science, vol. 21, no. 6, 2017, pp. 1454-62, doi:10.16984/saufenbilder.331327.
Vancouver Özmen N. Some new properties of the Meixner polynomials. SAUJS. 2017;21(6):1454-62.