establishing a parametric theta function and studying its characteristics in mathematical physics

In this paper, a new parametric (spectral) theta function formula in mathematical physics to have moreversatility in conformal quantum field theory is established. in this regard, we define and present the key eq. [5]as well as giving quasi-periodic characteristics of these parametric functions that perfectly covers many of thepast identities on jacobi theta functions. afterwards, for the first time, we explore new identities for themultiplication of the jacobi theta functions as bi-productions. finally, differentiation formulas of jacobi thetafunctions are presented spectrally.