In this paper, we introduce a new class of generalized extended Laguerre-based Apostol-type-Bernoulli, Apostol-type-Euler and Apostoltype-Genocchi polynomials. These Apostol type polynomials are used to connect Fubini-Hermite Bell-Hermite find representations. We derive some implicit summation formulae symmetric identities for these families special functions by applying the generating functions.

We introduce two sine and cosine types of generating functions in a general case apply them to the classical hypergeometric orthogonal polynomials as well some widely investigated combinatorial numbers such Bernoulli, Euler Genocchi numbers. This approach can also be applied other celebrated sequences.

In this research, we use operational matrix based on Genocchi polynomials to obtain approximate solutions for a class of fractional optimal control problems. The solution takes the form product consisting unknown coefficients and polynomials. Our main task is compute numerical values coefficients. To achieve goal, apply initial condition problem, Tau Lagrange multiplier methods. We do error ana...

Asymptotic approximation formulas for polynomials of the type Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi with integer order real parameters are obtained via hyperbolic functions. The derivation is done using principle saddle point expansion appropriate function about a point.

evaluates to n(£) for r = 3. In the published solution [16], It was also noted that Sx{n) = n(£), and, as a consequence, It was conjectured that S2r+i(n) equals the product of („) and a monk polynomial of degree r +1. We show this conjecture to be true, albeit with the modification of discarding the adjec-tival modifier monic. In fact, we show that S2r+l(n) = Pr(n)n(£) and S2r() = Qr()2~\ where...

have numerous important applications in number theory, combinatorics, and numerical analysis, among other areas, [1–13]. It is easy to find the values G1 = 1, G3 = G5 = G7 = ··· = 0, and even coefficients are given by G2m = 2(1− 2)B2n = 2nE2n−1(0), where Bn is a Bernoulli number and En(x) is an Euler polynomial. The first few Genocchi numbers for n= 2,4, . . . are −1,−3,17,−155,2073, . . . . Th...