Hahn-Appell polynomials and their d-orthogonality

---

Atıf İçin Kopyala

VARMA S., Yasar B. Y., Ozarslan M. A.

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, cilt.113, sa.3, ss.2127-2143, 2019 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 113 Sayı: 3
• Basım Tarihi: 2019
• Doi Numarası: 10.1007/s13398-018-0607-8
• Dergi Adı: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Sayfa Sayıları: ss.2127-2143
• Anahtar Kelimeler: Appell polynomials, Exponential function, Recurrence relation, d-Orthogonal polynomials, Linear functionals
• Ankara Üniversitesi Adresli: Evet

Özet

Recently, parametric (q,)-exponential functions were defined in [4]. In the present paper, we obtain non-parametric Hahn exponential functions by using the characteristic properties of the usual discrete and q-exponential functions. We introduce Hahn-Appell polynomials and prove that their generating function is written by means of this new non-parametric exponential function. We further obtain a recurrence relation, difference equation and determinantal representation of Hahn-Appell polynomials. Finally, we determine the generating function of the Hahn-Appell polynomials which are also d-orthogonal and obtain the form of d-dimensional functional vector which ensures the d- orthogonality.