Cuprate superconductivity: Dependence of T_c on the c-axis layering structure

The difference ΔT_c⁽ⁿ⁾ of the transition temperature for the nth member from the single layer value is given by ΔT_c⁽ⁿ⁾ = const×(1-1/n) is shown for identically doped members of the same homologous series without relying on any `mode' of the in-plane behavior of the electrons in either the normal or the superconducting state. Large changes in the electron energy loss spectroscopy and optical properties in the midinfrared regime on entering the superconducting state is predicted and stated that the basic mechanism of superconductivity in the cuprates has a large contribution from the small-q regime.