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