Recently the new q-Euler numbers and polynomials related to Frobenius-Euler numbers and polynomials are constructed by Kim (see[3]). In this paper, we study the generalized q-Euler numbers and polynomials attached to χ related to the new q-Euler numbers and polynomials which is constructed in [3]. Finally, we will derive some interesting congruence on the generalized q-Euler numbers and polynom...

We obtain an extension of the Christoffel–Darboux formula for matrix orthogonal polynomials with a generalized Hankel symmetry, including the Adler-van Moerbeke generalized orthogonal polynomials.

In this paper, we observe the behavior of complex roots of the generalized Euler polynomials Ẽn(x) of the second kind, using numerical investigation. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the generalized Euler polynomials Ẽn(x) of the second kind. Finally, we give a table for the solutions of the generalized Euler polynomials Ẽn...

in this paper, operational matrices of riemann-liouville fractional integration and caputo fractional differentiation for shifted jacobi polynomials are considered. using the given initial conditions, we transform the fractional differential equation (fde) into a modified fractional differential equation with zero initial conditions. next, all the existing functions in modified differential equ...

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...