Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2022, Cilt: 51 Sayı: 6, 1680 - 1696, 01.12.2022
https://doi.org/10.15672/hujms.799211

Öz

Kaynakça

  • [1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. Reprint of the 1972 Edition, Dover Publications, New York, 1992.
  • [2] Y. B. Cheikh, Some results on quasi-monomiality, Appl. Math. Comput. 141, 63-76, 2003.
  • [3] L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, Springer Science & Business Media, Heidelberg, Germany, 2012.
  • [4] F.A. Costabile and E. Longo, An algebraic approach to Sheffer polynomial sequences, Integral Transform. Spec. Funct. 25 (4), 295-311, 2014.
  • [5] G. Dattoli, P. Ricci, C. Cesarano and L. Vázquez, Special polynomials and fractional calculus, Math. Comput. Model. 37 (7-8), 729-733, 2003.
  • [6] N. Dunford and J. T. Schwartz, Linear Operators Part I: General Theory, vol. 243, Interscience publishers, New York, 1958.
  • [7] S. Khan and A. A. Al-Gonah, Multi-variable Hermite matrix polynomials: Properties and applications, J. Math. Anal. Appl. 412 (1), 222-235, 2014.
  • [8] S. Khan and T. Nahid, Connection problems and matrix representations for certain hybrid polynomials, Tbilisi Math. J. 11 (3), 81-93, 2018.
  • [9] W. Magnus, F. Oberhettinger and R. P. Soni, Formulas and Theorems For the Special Functions of Mathematical Physics, vol. 52, Springer Science & Business Media, Heidelberg, Germany, 2013.
  • [10] P. Natalini, G. Bretti and P. E. Ricci, Adjoint Hermite and Bernoulli polynomials, Bull. Allahabad Math. Soc. (Dharma Prakash Gupta Memorial Volume) 33 (2), 251- 264, 2018.
  • [11] P. Natalini and P. E. Ricci, Bell-Sheffer polynomial sets, Axioms 7 (4), 71, 2018.
  • [12] K. Oldham and J. Spanier, The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order, vol. 111, Academic Press, New York, 1974.
  • [13] S. Pinelas and P.E. Ricci, On Sheffer polynomial families, 4Open 2, 4, 2019.
  • [14] S. Roman, The Umbral Calculus, Academic Press, New York, 1984.
  • [15] L. W. Shapiro, S. Getu, W. J. Woan and L. C. Woodson, The riordan group, Discret. Appl. Math. 34 (1-3), 229-239, 1991.
  • [16] H. Srivastava and H. Manocha, Treatise on Generating Functions, John Wiley & Sons, New York, 1984.
  • [17] W. Wang, A determinantal approach to Sheffer sequences, Linear Algebra Appl. 463, 228-254, 2014.
  • [18] W. Wang and T. Wang, Generalized Riordan arrays, Discret. Math. 308 (24), 6466- 6500, 2008.
  • [19] G. Yasmin, H. Islahi and S. Araci, Finding mixed families of special polynomials associated with Gould-Hopper matrix polynomials, J. Inequal. Spec. Funct. 11 (1), 43-63, 2020.
  • [20] G. Yasmin and S. Khan, Hermite matrix based polynomials of two variables and Lie algebraic techniques, South East Asian Bull. Math. 38 , 603-618, 2014.
  • [21] G. Yasmin, S. A. Wani and H. Islahi, Finding hybrid families of special matrix polynomials associated with Sheffer sequences, Tbilisi Math. J. 12 (4), 43-59, 2019.

Certain results on hybrid relatives of the Sheffer polynomials

Yıl 2022, Cilt: 51 Sayı: 6, 1680 - 1696, 01.12.2022
https://doi.org/10.15672/hujms.799211

Öz

The multi-variable special matrix polynomials have been identified significantly both in mathematical and applied frameworks. Due to its usefulness and various applications, a variety of its extensions and generalizations have been investigated and presented. The purpose of the paper is intended to study and emerge with a new generalization of Hermite matrix based Sheffer polynomials by involving integral transforms and some known operational rules. Their properties and quasi-monomial nature are also established. Further, these sequences are expressed in determinant forms by utilizing the relationship between the Sheffer sequences and Riordan arrays. An analogous study of these results is also carried out for certain members belonging to generalized Hermite matrix based Sheffer polynomials.

Kaynakça

  • [1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables. Reprint of the 1972 Edition, Dover Publications, New York, 1992.
  • [2] Y. B. Cheikh, Some results on quasi-monomiality, Appl. Math. Comput. 141, 63-76, 2003.
  • [3] L. Comtet, Advanced Combinatorics: The Art of Finite and Infinite Expansions, Springer Science & Business Media, Heidelberg, Germany, 2012.
  • [4] F.A. Costabile and E. Longo, An algebraic approach to Sheffer polynomial sequences, Integral Transform. Spec. Funct. 25 (4), 295-311, 2014.
  • [5] G. Dattoli, P. Ricci, C. Cesarano and L. Vázquez, Special polynomials and fractional calculus, Math. Comput. Model. 37 (7-8), 729-733, 2003.
  • [6] N. Dunford and J. T. Schwartz, Linear Operators Part I: General Theory, vol. 243, Interscience publishers, New York, 1958.
  • [7] S. Khan and A. A. Al-Gonah, Multi-variable Hermite matrix polynomials: Properties and applications, J. Math. Anal. Appl. 412 (1), 222-235, 2014.
  • [8] S. Khan and T. Nahid, Connection problems and matrix representations for certain hybrid polynomials, Tbilisi Math. J. 11 (3), 81-93, 2018.
  • [9] W. Magnus, F. Oberhettinger and R. P. Soni, Formulas and Theorems For the Special Functions of Mathematical Physics, vol. 52, Springer Science & Business Media, Heidelberg, Germany, 2013.
  • [10] P. Natalini, G. Bretti and P. E. Ricci, Adjoint Hermite and Bernoulli polynomials, Bull. Allahabad Math. Soc. (Dharma Prakash Gupta Memorial Volume) 33 (2), 251- 264, 2018.
  • [11] P. Natalini and P. E. Ricci, Bell-Sheffer polynomial sets, Axioms 7 (4), 71, 2018.
  • [12] K. Oldham and J. Spanier, The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order, vol. 111, Academic Press, New York, 1974.
  • [13] S. Pinelas and P.E. Ricci, On Sheffer polynomial families, 4Open 2, 4, 2019.
  • [14] S. Roman, The Umbral Calculus, Academic Press, New York, 1984.
  • [15] L. W. Shapiro, S. Getu, W. J. Woan and L. C. Woodson, The riordan group, Discret. Appl. Math. 34 (1-3), 229-239, 1991.
  • [16] H. Srivastava and H. Manocha, Treatise on Generating Functions, John Wiley & Sons, New York, 1984.
  • [17] W. Wang, A determinantal approach to Sheffer sequences, Linear Algebra Appl. 463, 228-254, 2014.
  • [18] W. Wang and T. Wang, Generalized Riordan arrays, Discret. Math. 308 (24), 6466- 6500, 2008.
  • [19] G. Yasmin, H. Islahi and S. Araci, Finding mixed families of special polynomials associated with Gould-Hopper matrix polynomials, J. Inequal. Spec. Funct. 11 (1), 43-63, 2020.
  • [20] G. Yasmin and S. Khan, Hermite matrix based polynomials of two variables and Lie algebraic techniques, South East Asian Bull. Math. 38 , 603-618, 2014.
  • [21] G. Yasmin, S. A. Wani and H. Islahi, Finding hybrid families of special matrix polynomials associated with Sheffer sequences, Tbilisi Math. J. 12 (4), 43-59, 2019.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Ghazala Yasmin 0000-0003-0507-8950

Hibah Islahi Bu kişi benim 0000-0002-2718-4941

Yayımlanma Tarihi 1 Aralık 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 51 Sayı: 6

Kaynak Göster

APA Yasmin, G., & Islahi, H. (2022). Certain results on hybrid relatives of the Sheffer polynomials. Hacettepe Journal of Mathematics and Statistics, 51(6), 1680-1696. https://doi.org/10.15672/hujms.799211
AMA Yasmin G, Islahi H. Certain results on hybrid relatives of the Sheffer polynomials. Hacettepe Journal of Mathematics and Statistics. Aralık 2022;51(6):1680-1696. doi:10.15672/hujms.799211
Chicago Yasmin, Ghazala, ve Hibah Islahi. “Certain Results on Hybrid Relatives of the Sheffer Polynomials”. Hacettepe Journal of Mathematics and Statistics 51, sy. 6 (Aralık 2022): 1680-96. https://doi.org/10.15672/hujms.799211.
EndNote Yasmin G, Islahi H (01 Aralık 2022) Certain results on hybrid relatives of the Sheffer polynomials. Hacettepe Journal of Mathematics and Statistics 51 6 1680–1696.
IEEE G. Yasmin ve H. Islahi, “Certain results on hybrid relatives of the Sheffer polynomials”, Hacettepe Journal of Mathematics and Statistics, c. 51, sy. 6, ss. 1680–1696, 2022, doi: 10.15672/hujms.799211.
ISNAD Yasmin, Ghazala - Islahi, Hibah. “Certain Results on Hybrid Relatives of the Sheffer Polynomials”. Hacettepe Journal of Mathematics and Statistics 51/6 (Aralık 2022), 1680-1696. https://doi.org/10.15672/hujms.799211.
JAMA Yasmin G, Islahi H. Certain results on hybrid relatives of the Sheffer polynomials. Hacettepe Journal of Mathematics and Statistics. 2022;51:1680–1696.
MLA Yasmin, Ghazala ve Hibah Islahi. “Certain Results on Hybrid Relatives of the Sheffer Polynomials”. Hacettepe Journal of Mathematics and Statistics, c. 51, sy. 6, 2022, ss. 1680-96, doi:10.15672/hujms.799211.
Vancouver Yasmin G, Islahi H. Certain results on hybrid relatives of the Sheffer polynomials. Hacettepe Journal of Mathematics and Statistics. 2022;51(6):1680-96.