  For functions defined via Dirichlet/generalized Dirichlet series in some half
planes of the complex plane, we give a new simple elementary approach to obtain
an Approximate Functional Equation(AFE for short) for the product of functions
with explicit remainder term. We do this,using a highly generalized identity
following Motohashi's approach,wherein he uses a generalisation of Dirichlet's
device.We use our method to give an AFE for the product of two Dirichlet
L-series corresponding to primitive Dirichlet characters with hitherto unknown
estimate for its remainder term.We also consideer AFEs of functions on the real
line and the AFEs not only of the r-th power of Dirichlet L-series(or,of
Riemann Zeta function)but also of the r-th root of it,where r is a positive
integer
