Some identities on the q-Euler polynomials of higher order and q-stirling numbers by the fermionic p-adic integral on ℤp

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A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials (2012, unknown): “. Kim: (1.1) I− 1(f) = Z Z p f (ξ)dµ− (ξ) = lim N→∞ pXN−1 ξ=0 f (ξ)(−1)ξ . From (1.1), we have well known the following equality: (1.2) I−1(f1) +I−1(f) = 2f (0) here f1(x) := f (x+1) (for details, see[3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]). 2000 Mathematics”
Identities involving Frobenius–Euler polynomials arising from non-linear differential equations (2012, methodology): “ −u | {z } r− times ext = X∞ n=0 H(r) n (x | u) tn n! for u ∈ Cwith u 6= 1 . (6) In the special case, x = 0, H(r) n (0 | u) = H (r) n (u) are called the n-th Frobenius-Euler numbers of order r (see [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]). In this paper we derive non-linear diﬀerential ”