and are harmonic functions.Their series can be given as,
Here, we can see that both the above series have maximum magnitude -: . The speciality of both the functions is that there is and signs alternatively. Thats why for any big or small values of , both the above series converges to in magnitude.
Now, if we look at the expansion of ,
Here also the same situation occurs. But why it is not a function like and ? Why its value is not repeated like and ?