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Some new d-orthogonal polynomial sets of Sheffer type

Yıl 2019, Cilt: 68 Sayı: 1, 913 - 922, 01.02.2019

Serhan Varma

https://doi.org/10.31801/cfsuasmas.488383
Cited By: 5

Öz

In this paper, we present some new Sheffer type d-orthogonal polynomial sets. Moreover, we obtain the d-dimensional functional vector ensuring the d-orthogonality of these new polynomial sets.

Anahtar Kelimeler

Orthogonal polynomials d-orthogonal polynomials Sheffer polynomials generating function linear functionals

Kaynakça

  • Van Iseghem J., Vector orthogonal relations. Vector QD-algorithm, J. Comput. Appl. Math., 19 (1987) 141-150.
  • Maroni, P., L'orthogonalit`e et les recurrences de polynomes d'ordre superieur`a deux, Ann. Fac. Sci. Toulouse, 10 (1989), 105-139.
  • Chihara, T. S. An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, NY, 1978.
  • Ben Cheikh, Y. and Ben Romdhane N., On d-symmetric classical d-orthogonal polynomials, J. Comput. Appl. Math., 236 (2011), 85--93.
  • Ben Cheikh, Y. and Ben Romdhane N., d-symmetric d-orthogonal polynomials of Brenke type, J. Math. Anal. Appl., 416 (2014), 735--747.
  • Ben Cheikh, Y. and Douak K., On the classical d-orthogonal polynomials defined by certain generating functions I, Bull. Belg. Math. Soc. 7 (2000), 107-124.
  • Ben Cheikh, Y. and Douak K., On the classical d-orthogonal polynomials defined by certain generating functions II, Bull. Belg. Math. Soc. 8 (2001), 591-605.
  • Ben Cheikh, Y. and Gaied M., Dunkl-Appell d-orthogonal polynomials, Integral Transforms Spec. Funct. 18 (2007), 581--597.
  • Ben Cheikh, Y. and Gaied M., A Dunkl-classical d-symmetric d-orthogonal polynomial set, Rend. Mat. Appl. 30 (2010), 195--219.
  • Ben Cheikh, Y. and Gaied M., A characterization of Dunkl-classical d-symmetric d-orthogonal polynomials and its applications, J. Comput. Appl. Math. 236 (2011), 49--64.
  • Ben Cheikh, Y., Lamiri I. and Ouni A., On Askey-scheme and d-orthogonality. I. A characterization theorem, J. Comput. Appl. Math., 233 (2009), 621--629.
  • Ben Cheikh, Y. and Ouni A., Some generalized hypergeometric d-orthogonal polynomial sets, J. Math. Anal. Appl. 343 (2008), 464-478.
  • Ben Cheikh, Y. and Zaghouani A., Some discrete d-orthogonal polynomial sets, J. Comput. Appl. Math., 156 (2003), 253-263.
  • Ben Cheikh, Y. and Zaghouani A. d-Orthogonality via generating functions, J. Comput. Appl. Math. 199 (2007), 2-22.
  • Ben Romdhane, N., d-orthogonal Faber polynomials. Integral Transforms Spec, Funct. 18 (2007), 663--677.
  • Douak, K., The relation of the d-orthogonal polynomials to the Appell polynomials, J. Comput. Appl. Math., 70 (1996), 279--295.
  • Douak, K. and Maroni P., On d-orthogonal Tchebychev polynomials. I, Appl. Numer. Math., 24 (1997), 23--53.
  • Douak, K, Maroni P., On d-orthogonal Tchebychev polynomials. II, Methods Appl. Anal. 4 (1997), 404--429.
  • Lamiri, I., d-orthogonality of discrete q-Hermite type polynomials, J. Approx. Theory 170 (2013), 116--133.
  • Lamiri, I. and Ouni A., d-orthogonality of Humbert and Jacobi type polynomials, J. Math. Anal. Appl., 341 (2008), 24--51.
  • Lamiri, I. and Ouni A., d-orthogonality of Hermite type polynomials, Appl. Math. Comput., 202 (2008), 24--43.
  • Varma, S. and Taşdelen, F., On a different kind of d-orthogonal polynomials that generalize the Laguerre polynomials, Math. Æterna, 2 (2012), 561--572.
  • Zaghouani, A., Some basic d-orthogonal polynomial sets, Georgian Math. J., 12 (2005), 583--593.
  • Roman, S. The theory of the umbral calculus, I. J. Math. Anal. Appl. 87 (1982), 58--115.
  • Boas, R. and Buck, R. C., Polynomial expansions of analytic functions. Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge. Heft 19 Springer-Verlag, Berlin-Göttingen-Heidelberg; 1958.
  • Ben Cheikh, Y. and Gam, I., On some operators varying the dimensional parameters of d-orthogonality. Integral Transforms Spec. Funct., 27(9) (2016), 731-746.
  • Meixner, J., Orthogonale Polynomsysteme mit einer besonderen Gestalt der erzeugen den Funktionen, J. London Math. Soc., 9 (1934), 6 -- 13.
  • Sheffer, I. M., Some properties of polynomials of type zero, Duke Math. J., 5 (1939), 590 -- 622.
  • Al-Salam, W. A., Characterization theorems for orthogonal polynomials. Orthogonal polynomials (Columbus, OH, 1989), 1--24, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 294, Kluwer Acad. Publ., Dordrecht; 1990.
  • Boukhemis, A. and Maroni P., Une caractérisation des polynômes strictement 1/p orthogonaux de type Sheffer. Etude du cas p= 2, J. Approx. Theory., (1988), 54: 67--91.
  • Ben Cheikh, Y., Some results on quasi-monomiality. Advanced special functions and related topics in differential equations (Melfi, 2001), Appl. Math. Comput., (2003), 141: 63--76.
  • Ben Cheikh, Y., On obtaining dual sequences via quasi-monomiality, Georgian Math. J., 9 (2002), 413-422.

Yıl 2019, Cilt: 68 Sayı: 1, 913 - 922, 01.02.2019

Serhan Varma

https://doi.org/10.31801/cfsuasmas.488383
Cited By: 5

Öz

Kaynakça

  • Van Iseghem J., Vector orthogonal relations. Vector QD-algorithm, J. Comput. Appl. Math., 19 (1987) 141-150.
  • Maroni, P., L'orthogonalit`e et les recurrences de polynomes d'ordre superieur`a deux, Ann. Fac. Sci. Toulouse, 10 (1989), 105-139.
  • Chihara, T. S. An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, NY, 1978.
  • Ben Cheikh, Y. and Ben Romdhane N., On d-symmetric classical d-orthogonal polynomials, J. Comput. Appl. Math., 236 (2011), 85--93.
  • Ben Cheikh, Y. and Ben Romdhane N., d-symmetric d-orthogonal polynomials of Brenke type, J. Math. Anal. Appl., 416 (2014), 735--747.
  • Ben Cheikh, Y. and Douak K., On the classical d-orthogonal polynomials defined by certain generating functions I, Bull. Belg. Math. Soc. 7 (2000), 107-124.
  • Ben Cheikh, Y. and Douak K., On the classical d-orthogonal polynomials defined by certain generating functions II, Bull. Belg. Math. Soc. 8 (2001), 591-605.
  • Ben Cheikh, Y. and Gaied M., Dunkl-Appell d-orthogonal polynomials, Integral Transforms Spec. Funct. 18 (2007), 581--597.
  • Ben Cheikh, Y. and Gaied M., A Dunkl-classical d-symmetric d-orthogonal polynomial set, Rend. Mat. Appl. 30 (2010), 195--219.
  • Ben Cheikh, Y. and Gaied M., A characterization of Dunkl-classical d-symmetric d-orthogonal polynomials and its applications, J. Comput. Appl. Math. 236 (2011), 49--64.
  • Ben Cheikh, Y., Lamiri I. and Ouni A., On Askey-scheme and d-orthogonality. I. A characterization theorem, J. Comput. Appl. Math., 233 (2009), 621--629.
  • Ben Cheikh, Y. and Ouni A., Some generalized hypergeometric d-orthogonal polynomial sets, J. Math. Anal. Appl. 343 (2008), 464-478.
  • Ben Cheikh, Y. and Zaghouani A., Some discrete d-orthogonal polynomial sets, J. Comput. Appl. Math., 156 (2003), 253-263.
  • Ben Cheikh, Y. and Zaghouani A. d-Orthogonality via generating functions, J. Comput. Appl. Math. 199 (2007), 2-22.
  • Ben Romdhane, N., d-orthogonal Faber polynomials. Integral Transforms Spec, Funct. 18 (2007), 663--677.
  • Douak, K., The relation of the d-orthogonal polynomials to the Appell polynomials, J. Comput. Appl. Math., 70 (1996), 279--295.
  • Douak, K. and Maroni P., On d-orthogonal Tchebychev polynomials. I, Appl. Numer. Math., 24 (1997), 23--53.
  • Douak, K, Maroni P., On d-orthogonal Tchebychev polynomials. II, Methods Appl. Anal. 4 (1997), 404--429.
  • Lamiri, I., d-orthogonality of discrete q-Hermite type polynomials, J. Approx. Theory 170 (2013), 116--133.
  • Lamiri, I. and Ouni A., d-orthogonality of Humbert and Jacobi type polynomials, J. Math. Anal. Appl., 341 (2008), 24--51.
  • Lamiri, I. and Ouni A., d-orthogonality of Hermite type polynomials, Appl. Math. Comput., 202 (2008), 24--43.
  • Varma, S. and Taşdelen, F., On a different kind of d-orthogonal polynomials that generalize the Laguerre polynomials, Math. Æterna, 2 (2012), 561--572.
  • Zaghouani, A., Some basic d-orthogonal polynomial sets, Georgian Math. J., 12 (2005), 583--593.
  • Roman, S. The theory of the umbral calculus, I. J. Math. Anal. Appl. 87 (1982), 58--115.
  • Boas, R. and Buck, R. C., Polynomial expansions of analytic functions. Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge. Heft 19 Springer-Verlag, Berlin-Göttingen-Heidelberg; 1958.
  • Ben Cheikh, Y. and Gam, I., On some operators varying the dimensional parameters of d-orthogonality. Integral Transforms Spec. Funct., 27(9) (2016), 731-746.
  • Meixner, J., Orthogonale Polynomsysteme mit einer besonderen Gestalt der erzeugen den Funktionen, J. London Math. Soc., 9 (1934), 6 -- 13.
  • Sheffer, I. M., Some properties of polynomials of type zero, Duke Math. J., 5 (1939), 590 -- 622.
  • Al-Salam, W. A., Characterization theorems for orthogonal polynomials. Orthogonal polynomials (Columbus, OH, 1989), 1--24, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 294, Kluwer Acad. Publ., Dordrecht; 1990.
  • Boukhemis, A. and Maroni P., Une caractérisation des polynômes strictement 1/p orthogonaux de type Sheffer. Etude du cas p= 2, J. Approx. Theory., (1988), 54: 67--91.
  • Ben Cheikh, Y., Some results on quasi-monomiality. Advanced special functions and related topics in differential equations (Melfi, 2001), Appl. Math. Comput., (2003), 141: 63--76.
  • Ben Cheikh, Y., On obtaining dual sequences via quasi-monomiality, Georgian Math. J., 9 (2002), 413-422.
Toplam 32 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Serhan Varma 0000-0003-0346-5738

Yayımlanma Tarihi 1 Şubat 2019
Gönderilme Tarihi 22 Mart 2017
Kabul Tarihi 27 Kasım 2018
Yayımlandığı Sayı Yıl 2019 Cilt: 68 Sayı: 1

Kaynak Göster

APA Varma, S. (2019). Some new d-orthogonal polynomial sets of Sheffer type. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 913-922. https://doi.org/10.31801/cfsuasmas.488383
AMA Varma S. Some new d-orthogonal polynomial sets of Sheffer type. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2019;68(1):913-922. doi:10.31801/cfsuasmas.488383
Chicago Varma, Serhan. “Some New D-Orthogonal Polynomial Sets of Sheffer Type”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, sy. 1 (Şubat 2019): 913-22. https://doi.org/10.31801/cfsuasmas.488383.
EndNote Varma S (01 Şubat 2019) Some new d-orthogonal polynomial sets of Sheffer type. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 913–922.
IEEE S. Varma, “Some new d-orthogonal polynomial sets of Sheffer type”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 1, ss. 913–922, 2019, doi: 10.31801/cfsuasmas.488383.
ISNAD Varma, Serhan. “Some New D-Orthogonal Polynomial Sets of Sheffer Type”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (Şubat 2019), 913-922. https://doi.org/10.31801/cfsuasmas.488383.
JAMA Varma S. Some new d-orthogonal polynomial sets of Sheffer type. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:913–922.
MLA Varma, Serhan. “Some New D-Orthogonal Polynomial Sets of Sheffer Type”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 68, sy. 1, 2019, ss. 913-22, doi:10.31801/cfsuasmas.488383.
Vancouver Varma S. Some new d-orthogonal polynomial sets of Sheffer type. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):913-22.

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