Mixing
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.
summation
asked yesterday
Joshhh
1,014410
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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
asked yesterday
Joshhh
1,014410
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
add a comment |
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
asked yesterday
Joshhh
1,014410
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
asked yesterday
Joshhh
1,014410
asked yesterday
Joshhh
1,014410
asked yesterday
Joshhh
1,014410
asked yesterday
Joshhh
1,014410
asked yesterday
Joshhh
1,014410
1,014410
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
add a comment |
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
add a comment |
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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