- #1

sanjibghosh

- 50

- 0

"

**sum of exponential of[-a^2.n^2**]" , where, n is an integer... and sum over 1 to infinity, and "

**a**" is "not small...", I've calculate two asymptotic behaviours , i,e when "

**a<<1**" , in this case I've integrated it and have got,

**sqrt(pi)/2a-1**, and in the limit

**a->infinity**, it is simply "0", so the actaul result may be,

**f(a)=sqrt(pi)/2a+g(a)**, but if g(a) contains

**a^(-m)**, where

**m>1**, then actually this would have dominated in the limit

**a->0**, but its not the case... so g(a) cannot contain the term...

**a^(-m)**, now if

**g(a)**contain a term like

**"a^m", m>1,**then in the limit

**a->infinity**we'd have got "

**infinity**" instead of "

**0**", so this is also not possible... and if here in "

**a^(-m) "m" is such that 1>m>0,**then we will get a complex result...for

**-ve "a"**but that is forbidden... as each term is real... how can the sum become complex... so I guess the result should be...

**"sqrt(pi)/2a**"... please help... (this problem occurred when I was calculating the partition function of particle in an 1-D box...)