Sum of series $sumlimits_{k=0}^infty frac{a^{k^2}}{k!}$
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-3
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I am looking at this sum:
$displaystylesum_{k=0}^infty frac{a^{(k^2)}}{k!}$ for some $a>0$.
sequences-and-series power-series
edited Dec 4 at 20:47
Did
245k23219453
asked Dec 4 at 19:49
E Onaran
62
add a comment |
up vote
-3
down vote
favorite
I am looking at this sum:
$displaystylesum_{k=0}^infty frac{a^{(k^2)}}{k!}$ for some $a>0$.
sequences-and-series power-series
edited Dec 4 at 20:47
Did
245k23219453
asked Dec 4 at 19:49
E Onaran
62
4
Hi and welcome to the Math.SE. Why this problem is interesting for you? And what did you tried in order to solve it? I you want to get help from other members, you should try to add as more context as possible to your question, in order to help them help you.
– Daniele Tampieri
Dec 4 at 19:52
add a comment |
up vote
-3
down vote
favorite
up vote
-3
down vote
favorite
I am looking at this sum:
$displaystylesum_{k=0}^infty frac{a^{(k^2)}}{k!}$ for some $a>0$.
sequences-and-series power-series
edited Dec 4 at 20:47
Did
245k23219453
asked Dec 4 at 19:49
E Onaran
62
I am looking at this sum:
$displaystylesum_{k=0}^infty frac{a^{(k^2)}}{k!}$ for some $a>0$.
sequences-and-series power-series
sequences-and-series power-series
edited Dec 4 at 20:47
Did
245k23219453
asked Dec 4 at 19:49
E Onaran
62
edited Dec 4 at 20:47
Did
245k23219453
asked Dec 4 at 19:49
E Onaran
62
edited Dec 4 at 20:47
Did
245k23219453
edited Dec 4 at 20:47
Did
245k23219453
edited Dec 4 at 20:47
Did
245k23219453
245k23219453
asked Dec 4 at 19:49
E Onaran
62
asked Dec 4 at 19:49
E Onaran
62
asked Dec 4 at 19:49
E Onaran
62
62
4
Hi and welcome to the Math.SE. Why this problem is interesting for you? And what did you tried in order to solve it? I you want to get help from other members, you should try to add as more context as possible to your question, in order to help them help you.
– Daniele Tampieri
Dec 4 at 19:52
add a comment |
4
Hi and welcome to the Math.SE. Why this problem is interesting for you? And what did you tried in order to solve it? I you want to get help from other members, you should try to add as more context as possible to your question, in order to help them help you.
– Daniele Tampieri
Dec 4 at 19:52
4
4
Hi and welcome to the Math.SE. Why this problem is interesting for you? And what did you tried in order to solve it? I you want to get help from other members, you should try to add as more context as possible to your question, in order to help them help you.
– Daniele Tampieri
Dec 4 at 19:52
Hi and welcome to the Math.SE. Why this problem is interesting for you? And what did you tried in order to solve it? I you want to get help from other members, you should try to add as more context as possible to your question, in order to help them help you.
– Daniele Tampieri
Dec 4 at 19:52
add a comment |
1 Answer
1
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oldest
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1
down vote
accepted
If I get to choose $a$ I choose $1$ and the sum is $e$.
For $a gt 1$ the sum diverges.
For $0 lt a lt 1$ it will converge quickly but I suspect has no easy answer. Alpha says that for $a=frac 12$ the sum is about $0.531576$ but does not give a closed form.
answered Dec 4 at 20:52
Ross Millikan
290k23195368
This is a special function, theta or something.
– Did
Dec 4 at 23:57
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
If I get to choose $a$ I choose $1$ and the sum is $e$.
For $a gt 1$ the sum diverges.
For $0 lt a lt 1$ it will converge quickly but I suspect has no easy answer. Alpha says that for $a=frac 12$ the sum is about $0.531576$ but does not give a closed form.
answered Dec 4 at 20:52
Ross Millikan
290k23195368
This is a special function, theta or something.
– Did
Dec 4 at 23:57
add a comment |
up vote
1
down vote
accepted
If I get to choose $a$ I choose $1$ and the sum is $e$.
For $a gt 1$ the sum diverges.
For $0 lt a lt 1$ it will converge quickly but I suspect has no easy answer. Alpha says that for $a=frac 12$ the sum is about $0.531576$ but does not give a closed form.
answered Dec 4 at 20:52
Ross Millikan
290k23195368
This is a special function, theta or something.
– Did
Dec 4 at 23:57
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
If I get to choose $a$ I choose $1$ and the sum is $e$.
For $a gt 1$ the sum diverges.
For $0 lt a lt 1$ it will converge quickly but I suspect has no easy answer. Alpha says that for $a=frac 12$ the sum is about $0.531576$ but does not give a closed form.
answered Dec 4 at 20:52
Ross Millikan
290k23195368
If I get to choose $a$ I choose $1$ and the sum is $e$.
For $a gt 1$ the sum diverges.
For $0 lt a lt 1$ it will converge quickly but I suspect has no easy answer. Alpha says that for $a=frac 12$ the sum is about $0.531576$ but does not give a closed form.
answered Dec 4 at 20:52
Ross Millikan
290k23195368
answered Dec 4 at 20:52
Ross Millikan
290k23195368
answered Dec 4 at 20:52
Ross Millikan
290k23195368
answered Dec 4 at 20:52
Ross Millikan
290k23195368
290k23195368
This is a special function, theta or something.
– Did
Dec 4 at 23:57
add a comment |
This is a special function, theta or something.
– Did
Dec 4 at 23:57
This is a special function, theta or something.
– Did
Dec 4 at 23:57
This is a special function, theta or something.
– Did
Dec 4 at 23:57
add a comment |
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Hi and welcome to the Math.SE. Why this problem is interesting for you? And what did you tried in order to solve it? I you want to get help from other members, you should try to add as more context as possible to your question, in order to help them help you.
– Daniele Tampieri
Dec 4 at 19:52