Welcome to a bit of TEX hacking.

[tex]\frac{(\frac{1+v^2}{c^2})}{2}[/tex] = [tex](\frac{1+v^2}{2c^2})[/tex]

However, it is not the same as:

[tex]\frac{c^2+v^2}{2c^2}[/tex] = [tex]\frac{1}{2} + \frac{v^2}{2c^2}[/tex]

Unless I missed something in the original equation.

I'll try to understand your equation later, but I assume you are doing something similar to the

Lorentz Transformation.

Velocity is a function of time and distance, thus

Time is a function of velocity and distance.

Hmmm,

So, is T

_{0} a constant (initial time), or is it a function (the time function independent of gravitation effects)?

M is the mass of the planet.

G is the gravitational constant.

R is distance from the center of the planet.

c is the speed of light.

v is the velocity of whatever is carrying the clock.

Of course, if you think of Earth, the planet surface where most of our clocks are is spinning and moving.

Anyway, why don't you post a little about what you're trying to accomplish, and the derivation of your equation.