Jacob's ladders, crossbreeding and new synergetic formulas for the class of more complicated external parts of $\zeta$-factorization formulas

Abstract

In this paper we obtain new canonical synergetic formula, namely an $\zeta$-analogue of next elementary trigonometric formula. This one describes cooperative interactions between corresponding class of elementary functions and the Riemann's zeta-function on a class of disconnected sets on the critical line.