So the series for e^{u} is Σ_{n} u^{n}/(n!)Hi.
I know that e^{ix}e^{-ix} = 1 but if I write the product of the 2 exponentials as infinite series I get
Σ_{n}Σ_{m} x^{n}/(n!) (-x)^{m}/(m!)
without knowing the result is 1 using exponentials how would I get the result of this product of 2 infinite sums ?
Thanks
Sure, you could do that for this particular problem, but this ignores the OP's question about the product of two infinite series.You may also use: ##e^{ix}=(cosx+isinx)## and symmetry properties of ##sinx, cosx##.