I am in a trouble to work out the sum, i.e.(adsbygoogle = window.adsbygoogle || []).push({});

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

f(a)=sqrt(pi)/2a+g(a), but if g(a) containsa^(-m), wherem>1, then actually this would have dominated in the limita->0, but its not the case... so g(a) cannot contain the term...a^(-m), now ifg(a)contain a term like"a^m", m>1,then in the limita->infinitywe'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".... plz help..... (this problem occured when I was calculating the partition function of particle in an 1-D box....)

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# Sum of exponential of (-a^2 n^2)

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