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In this paper, we introduce (p , q) -cosine Euler polynomials. From these polynomials, we find several properties and identities. Moreover, we find the circle equations of approximate roots for (p , q) -cosine Euler polynomials by using a computer. [ABSTRACT FROM AUTHOR]

This paper constructs and introduces (p , q) -cosine and (p , q) -sine Bernoulli polynomials using (p , q) -analogues of (x + a) n . Based on these polynomials, we discover basic properties and identities. Moreover, we determine special properties using (p , q) -trigonometric functions and verify various symmetric properties. Finally, we check the symmetric structure of the approximate roots based on symmetric polynomials. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]