/sci/ - Science & Math » Thread #12879057

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Sum of square roots of natural numbers?

Anonymous Thu 25 Mar 00:48:53 2021 No.12879057 View Reply Original Report

Quoted By: >>12879081

I've been trying to make an infinite polynomial that represents the function in the pic. Is it possible? I've been toying with this problem for a year. Any ideas?

Anonymous

Anonymous Thu 25 Mar 2021 00:50:38 No.12879062 Report

Quoted By: >>12879074 >>12879075

>infinite polynomial
wat

Anonymous

Anonymous Thu 25 Mar 2021 00:52:50 No.12879074 Report

Quoted By:

>>12879062
non integer exponent polynomial yes?

Anonymous

Anonymous Thu 25 Mar 2021 00:52:59 No.12879075 Report

Quoted By: >>12879097

>>12879062
There is no closed form solution to the sum. I can make rudimentary approximations but is there an infinitely long approximation that is exact, ya know? Like a Taylor series.

Anonymous

Anonymous Thu 25 Mar 2021 00:55:43 No.12879081 Report

Quoted By: >>12879089

>>12879057
Did you try (shifting the index,) using the binomial theorem and interchanging sums?

Anonymous

Anonymous Thu 25 Mar 2021 00:58:16 No.12879089 Report

Quoted By: >>12879095

>>12879081
Thank you brother. I have been raw dogging these big summations blind because real analysis is gay. I think that's a good jumping point.

I think I've been doing something similar but very informally.

Anonymous

Anonymous Thu 25 Mar 2021 01:00:45 No.12879095 Report

Quoted By:

>>12879089
https://en.wikipedia.org/wiki/Harmonic_number#Generalized_harmonic_numbers

Anonymous

Anonymous Thu 25 Mar 2021 01:02:30 No.12879097 Report

Quoted By:

>>12879075
I know what you meant, I just never heard it referred to that way.

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