Fourier expansion of periodic U-Bernoulli, U-Euler and U-Genocchi functions and their relation with the Riemann zeta function

Fourier series and generating function theory is an active branch of modern analysis that has gained importance due to its applications in methods of analysis for mathematical solutions to boundary value problems, engineering, and signal processing in communications. On the other hand, the Riemann zeta function and its generalizations are useful in the investigation of analytic number theory and allied disciplines, especially in the role played by their special values in integral arguments (see [4, 14]).