The product of 2 infinite sums

• I
Hi.
I know that eixe-ix = 1 but if I write the product of the 2 exponentials as infinite series I get
ΣnΣm xn/(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

fresh_42
Mentor
What do you get, if you do not ignore the ##i## as you did, and group the products by degree of ##x##?

scottdave
Homework Helper
Hi.
I know that eixe-ix = 1 but if I write the product of the 2 exponentials as infinite series I get
ΣnΣm xn/(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
So the series for eu is Σn un/(n!)
and u is either ix or -ix (in your example). But you lost the i when converting to the series.

Yes sorry I forgot the i when writing out the infinite series

WWGD