BILATERAL AND BILINEAR GENERATING FUNCTIONS FOR THE GENERALIZED ZERNIKE OR DISC POLYNOMIALS

AKTAŞ R., TAŞDELEN YEŞİLDAL F., Yavuz N.

ARS COMBINATORIA, cilt.111, ss.389-400, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 111
  • Basım Tarihi: 2013
  • Dergi Adı: ARS COMBINATORIA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.389-400
  • Anahtar Kelimeler: Jacobi polynomials, generalized Zernike polynomials, disc polynomials, generating function, bilinear generating function, bilateral generating function, FAMILIES
  • Ankara Üniversitesi Adresli: Evet

Özet

In this paper, we obtain some generating functions for the generalized Zernike or disk polynomials P-m,n(alpha) (z, z*) which are investigated by Wunsche [13]. We derive various families of bilinear and bilateral generating functions. Furthermore, some special cases of the results presented in this study are indicated. Also, it is possible to obtain multilinear and multilateral generating functions for the polynomials P-m,n(alpha) (z, z*).