Regularization of the following sum
$begingroup$
Am interested in how one could regularize the following sum
$sum_{m,n = 1, infty} sqrt{m^2 + n^2}$. Would preferably want this in the $epsilon$ expansion regularization as talked below where a series $sum_{n=1,infty} n$ is regularized by introducing $sum_{n=1,infty} n e^{-epsilon n}$
http://blog.wolfram.com/2014/08/06/the-abcd-of-divergent-series/
divergent-series
asked Jan 8 at 4:30
wasnikwasnik
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add a comment |
$begingroup$
Am interested in how one could regularize the following sum
$sum_{m,n = 1, infty} sqrt{m^2 + n^2}$. Would preferably want this in the $epsilon$ expansion regularization as talked below where a series $sum_{n=1,infty} n$ is regularized by introducing $sum_{n=1,infty} n e^{-epsilon n}$
http://blog.wolfram.com/2014/08/06/the-abcd-of-divergent-series/
divergent-series
asked Jan 8 at 4:30
wasnikwasnik
1
New contributor
wasnik is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
Am interested in how one could regularize the following sum
$sum_{m,n = 1, infty} sqrt{m^2 + n^2}$. Would preferably want this in the $epsilon$ expansion regularization as talked below where a series $sum_{n=1,infty} n$ is regularized by introducing $sum_{n=1,infty} n e^{-epsilon n}$
http://blog.wolfram.com/2014/08/06/the-abcd-of-divergent-series/
divergent-series
asked Jan 8 at 4:30
wasnikwasnik
1
New contributor
wasnik is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
Am interested in how one could regularize the following sum
$sum_{m,n = 1, infty} sqrt{m^2 + n^2}$. Would preferably want this in the $epsilon$ expansion regularization as talked below where a series $sum_{n=1,infty} n$ is regularized by introducing $sum_{n=1,infty} n e^{-epsilon n}$
http://blog.wolfram.com/2014/08/06/the-abcd-of-divergent-series/
divergent-series
divergent-series
asked Jan 8 at 4:30
wasnikwasnik
1
New contributor
wasnik is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 8 at 4:30
wasnikwasnik
1
New contributor
wasnik is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 8 at 4:30
wasnikwasnik
1
New contributor
wasnik is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Jan 8 at 4:30
wasnikwasnik
1
asked Jan 8 at 4:30
wasnikwasnik
1
1
New contributor
wasnik is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
wasnik is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
wasnik is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
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