Geometric sum with squared exponentials











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Is there a closed form of the following finite sum?
$$
sumlimits_{n=0}^{N}q^{n^2}
$$
where $q>0$. The only thing I found somehow related is the Jacobi $theta$ elliptic function, but there it is an infinite sum.






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  • 1




    If you can relate a summation to a special function, this is a good sign that no closed-form exists. Otherwise there would be no need for existence of the special function.
    – Yves Daoust
    23 hours ago















up vote
1
down vote

favorite












Is there a closed form of the following finite sum?
$$
sumlimits_{n=0}^{N}q^{n^2}
$$
where $q>0$. The only thing I found somehow related is the Jacobi $theta$ elliptic function, but there it is an infinite sum.






summation







share|cite|improve this question


















  • 1




    If you can relate a summation to a special function, this is a good sign that no closed-form exists. Otherwise there would be no need for existence of the special function.
    – Yves Daoust
    23 hours ago













up vote
1
down vote

favorite









up vote
1
down vote

favorite











Is there a closed form of the following finite sum?
$$
sumlimits_{n=0}^{N}q^{n^2}
$$
where $q>0$. The only thing I found somehow related is the Jacobi $theta$ elliptic function, but there it is an infinite sum.






summation







share|cite|improve this question













Is there a closed form of the following finite sum?
$$
sumlimits_{n=0}^{N}q^{n^2}
$$
where $q>0$. The only thing I found somehow related is the Jacobi $theta$ elliptic function, but there it is an infinite sum.






summation




summation






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked yesterday









Joshhh

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  • 1




    If you can relate a summation to a special function, this is a good sign that no closed-form exists. Otherwise there would be no need for existence of the special function.
    – Yves Daoust
    23 hours ago














  • 1




    If you can relate a summation to a special function, this is a good sign that no closed-form exists. Otherwise there would be no need for existence of the special function.
    – Yves Daoust
    23 hours ago








1




1




If you can relate a summation to a special function, this is a good sign that no closed-form exists. Otherwise there would be no need for existence of the special function.
– Yves Daoust
23 hours ago




If you can relate a summation to a special function, this is a good sign that no closed-form exists. Otherwise there would be no need for existence of the special function.
– Yves Daoust
23 hours ago















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