Insights Further Sums Found Through Fourier Series - Comments

Svein
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Further Sums Found Through Fourier Series
fourierseries2.png


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Quick Latex pointer: if you write "\left(" and "\right)" instead of "(" and ")" you get parentheses which self-adjust their height.
 
Mathematica gave this:

Sums.png
 
Last edited:
The Electrician said:
Mathematica gave this:
Then Mathematica and I agree. Fine!

For me this is part of the road I am currently going. As long as I am getting correct answers along the way, I am happy.
 
Svein said:
Then Mathematica and I agree. Fine!

For me this is part of the road I am currently going. As long as I am getting correct answers along the way, I am happy.

Did you notice that Mathematica disagrees on the sign of the last one?
 
The Electrician said:
Did you notice that Mathematica disagrees on the sign of the last one?
No, saw it just now. Mathematica is correct, the correct exponent for (-1) should be (n-1), not n.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

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