A Note on $(p,q)$-analogue Type of Frobenius-Genocchi Numbers and Polynomials

다국어 초록 (Multilingual Abstract)

The main purpose of this paper is to introduce Apostol type (p, q)-Frobenius-Genocchi numbers and polynomials of order α and inves- tigate some basic identities and properties for these polynomials and num- bers including addition theorems, difference equations, derivative proper- ties, recurrence relations. We also obtain integral representations, im- plicit and explicit formulas and relations for these polynomials and num- bers. Furthermore, we consider some relationships for Apostol type (p, q)- Frobenius-Genocchi polynomials of order α associated with (p, q)-Apostol Bernoulli polynomials, (p, q)-Apostol Euler polynomials and (p, q)-Apostol Genocchi polynomials.

참고문헌 (Reference)

1 W. A. Khan, "Some symmetric identities for the generalized Bernoulli, Euler and Genocchi polynomials associated with Hermite polynomials" 5 : 1-21, 2016

2 M. A. Pathan, "Some implicit summation formulas and symmetric identities for the generalized Hermite-Bernoulli polynomials" 12 : 679-695, 2015

3 Waseem Ahmad Khan, "Some Properties of the Generalized Apostol Type Hermite- Based Polynomials" 경북대학교 자연과학대학 수학과 55 (55): 597-614, 2015

4 V. Kurt, "On the generalized Apostol type Frobenius Euler polynomials" 2013 (2013): 1-9, 2013

5 P. N. Sadjang, "On the fundamental theorem of p; q-calculus and some (p; q)-Taylor for-mulas"

6 U. Duran, "On higher order(p; q)-Frobenius-Euler polynomials" 8 (8): 198-208, 2017

7 U. Duran, "On (p; q)-Bernoulli, (p; q)-Euler and (p; q)-Genocchi polynomials" 13 : 7833-7908, 2016

8 Waseem A. Khan, "ON HIGHER ORDER (p, q)-FROBENIUS-GENOCCHI NUMBERS AND POLYNOMIALS" 한국전산응용수학회 37 (37): 295-305, 2019

9 Y. Simsek, "Generating functions for q-Apostal type Frobenius-Euler number and polyno-mials" 1 : 395-403, 2012

10 Y. Simsek, "Generating functions for generalized Stirling type numbers, Array type poly-nomials, Eulerian type polynomials and their applications" 2013

11 B. Y. Yasar, "Frobenius-Euler and Frobenius-Genocchi polynomials and their differential equations" 3 (3): 172-180, 2015

12 L. Carlitz, "Eulerian numbers and polynomials" 32 : 164-171, 1959

13 V. Gupta, "Bernstein Durrmeyer operators and based on two parameters, Facta Universitatis (Nis)" 31 (31): 79-95, 2016

14 U. Duran, "Apostol type(p; q)-Frobenious-Euler polynomials and numbers" 42 (42): 555-567, 2018

15 U. Duran, "Apostol type (p; q)-Bernoulli, (p; q)-Euler and (p; q)-Genocchi polynomials and numbers" 8 (8): 7-30, 2017

16 H. M. Srivastava, "A treatise on generating functions" Ellis Horwood Limited. Co 1984

17 유천성, "A note on the Frobenius-Euler polynomials" 장전수학회 14 (14): 495-501, 2011

18 B. Kurt, "A note on the Apostal type q-Frobenius Euler polynomials and generalizations of the Srivastava-Pinter addition theorems" 30 (30): 65-72, 2016

19 W. A. Khan, "A new class of partially degenerate Hermite-Genocchi polynomials" 10 : 5072-5081, 2017

20 M. A. Pathan, "A new class of generalized polynomials associated with Hermite and Euler polynomials" 13 (13): 913-928, 2016

21 V. Gupta, "(p; q)-Baskakov-Kontorovich operators" 10 (10): 1551-1556, 2016