Complete sum of products of (h, q)-extension of Euler polynomials and numbers

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Simsek Y.

JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, cilt.16, sa.11, ss.1331-1348, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 16 Sayı: 11
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1080/10236190902813967
  • Dergi Adı: JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1331-1348
  • Anahtar Kelimeler: symmetry properties of the p-adic Volkenborn integral, q-Euler numbers and polynomials, multinomial theorem, Barnes' type multiple (h, q)-Euler zeta function, partial (h, q)-Euler zeta function, Q-BERNOULLI NUMBERS, ADIC Q-INTEGRALS, Q)-BERNOULLI NUMBERS, TWISTED (H, Z(P)
  • Akdeniz Üniversitesi Adresli: Evet

Özet

By applying the symmetry of the fermionic p-adic q-integral on [image omitted], which is defined by T. Kim, J. Difference Equ. Appl. 14(12) (2008), pp. 1267-1277, we give recurrence identities (h, q)-Euler polynomials and the alternating sums of powers of consecutive (h, q)-integers. By using the fermionic p-adic q-integral and multinomial theorem, we construct generating functions of the higher-order (h, q)-extension of Euler polynomials and numbers. By using these numbers and polynomials, we give new approach to the complete sums of products of (h, q)-extension of Euler polynomials and numbers. We define some identities involving (h, q)-extension of Euler polynomials and numbers. Furthermore, by applying derivative operator to the generating function of the (h, q)-Euler polynomials of higher-order, we construct Barnes' type multiple (h, q)-Euler zeta function. This function interpolates (h, q)-Euler polynomials of higher-order at negative integers. We also define multiple partial (h, q)-Euler zeta function which interpolates the numbers [image omitted] at negative integers.