I am looking forward for an answer to your question as well. May be you should ask it on another discussion section of the forum like "Digital communication".
Why would you want to use a Taylor series to prove the transmission equation. However I suppose that you could simply do the math using trigonometric functions to account for the phase effects and use the standard decay for the amplitude.
By repeating the process for both the LOS and the reflected paths you should en up with a series of trigonometric functions this can then be transformed into a Taylor series?