Geodesic
Apostol Type $\left( p,q\right) $-Frobenius-Euler Polynomials and Numbers
Kragujevac Journal of Mathematics, Tome 42 (2018) no. 4, p. 555

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In the present paper, we introduce $\left( p,q\right) $-extension of Apostol type Frobenius-Euler polynomials and numbers and investigate some basic identities and properties for these polynomials and numbers, including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, explicit formulas and relations for these polynomials and numbers. Moreover, we discover $\left( p,q\right) $-extensions of Carlitz's result [L. Carlitz, Mat. Mag. { 32} (1959), 247-260] and Srivastava and Pintér addition theorems in [H. M. Srivastava, A. Pinter, Appl. Math. Lett. { 17} (2004), 375-380].
Classification : 05A30 11B68, 11B73
Keywords: $\left( p;q\right) $-calculus, Bernoulli polynomials, Euler polynomials, Genocchi polynomials, Frobenius-Euler polynomials, generating function, Cauchy product 
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     author = {Ugur Duran and Mehmet Acikgoz},
     title = {Apostol {Type} $\left( p,q\right) ${-Frobenius-Euler} {Polynomials} and {Numbers}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {555 },
     publisher = {mathdoc},
     volume = {42},
     number = {4},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2018_42_4_a7/}
}
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Ugur Duran; Mehmet Acikgoz. Apostol Type $\left( p,q\right) $-Frobenius-Euler Polynomials and Numbers. Kragujevac Journal of Mathematics, Tome 42 (2018) no. 4, p. 555 . http://geodesic.mathdoc.fr/item/KJM_2018_42_4_a7/