Mellin transformation and its application on Zeta function
Mellin transformation is a kind of integral transformation with power function as integral kernel,which is often used in the research of generalized residue theorem,signal processing and progressive expansion theory.Based on Mellin transformation theory and the relationship between Mellin transformation,Fourier transformation and Zeta function,the transformation form of Mellin transformation in the multiplication of Zeta function and Gamma function is derived.The application method and technique of Mellin transformation in Zeta function transformation are discussed in detail with Euler product formula.
Mellin transformationFourier transformZeta functionHurwitz Zeta function