Playing around with summations

1. Oct 30, 2013

Hazzattack

Hi guys, i'm hoping someone could explain this for me... and was also hoping that some decent literature could be suggested to help me get more comfortable with series expansions of things etc...

So i was playing around with the Q function (its used in quantum optics) and in the book they say that;

For the sum from 0 to infinity Ʃn^n = 1

(the bold case n's represent 'average' values - not sure if that makes a difference?)

Why is this the case ?

Thanks to anyone who can shed some light on this.

Last edited: Oct 30, 2013
2. Oct 30, 2013

Office_Shredder

Staff Emeritus
Can you explain what you mean by average values? Is n totally independent of n here?

3. Oct 30, 2013

Hazzattack

I think the index of the sum only applies to the power and not to the average value. (which i think is what you mean by them being independent?

In this case the sum represents the photon distribution where n represents the average photon number, so i'm assuming it doesn't make sense to sum over that?

Sorry if that isn't very clear...

4. Oct 30, 2013

Hazzattack

5. Oct 30, 2013

Hazzattack

Never mind i've realised why. Thanks for anyone who took a look.