In this paper, we define cosine Bernoulli polynomials and sine Bernoulli polynomials related to the q-number. Furthermore, we intend to find the properties of these polynomials and check the structure of the roots. Through numerical experimentation, we look for various assumptions about the polynomials above.

In this paper, we define the modified higher-order degenerate q-Euler polynomials and give some identities for these polynomials. Also we give numerical investigations of the zeroes of the modified higher-order q-Euler polynomials and the zeroes of the modified higher-order degenerate q-Euler polynomials.Furthermore, we demonstrate the shapes and zeroes of the modified higher-order q-Euler polynomials and the modified higher-order degenerate q-Euler polynomials by using a computer.

We constructed generating functions of the second kind (h, q)-Euler polynomials and numbers of higher order by using the fermionic p-adic integral. By using these numbers and polynomials, we give new approach to the complete sums of products of the second kind (h, q)-Euler polynomials and numbers of higher order.