Talk:Pi Squared is Irrational/Proof 2
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The proof has several errors - one is here:
Let us define a polynomial:
- $\ds \map f x = \frac {\paren {1 - x^2}^n} {n!} = \sum_{m \mathop = n}^{2 n} \frac {c_m} {n!} x^m$
for $c_m \in \Z$.
If $n = 1$
\(\ds \map f x\) | \(=\) | \(\ds \frac {\paren {1 - x^2} } {1!}\) | $n = 1$ | |||||||||||
\(\ds \sum_{m \mathop = n}^{2 n} \frac {c_m} {n!} x^m\) | \(=\) | \(\ds \sum_{m \mathop = 1}^2 \frac {c_m} {1!} x^m\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds c_1 x + c_2 x^2\) |
This would correct the issue:
- $\ds \map f x = \frac {\paren {1 - x^2}^n} {n!} = \sum_{m \mathop = 0}^n \frac {c_m} {n!} x^{2 m}$
for $c_m \in \Z$.
There are additional errors similar to this one. --Robkahn131 (talk) 21:39, 16 April 2024 (UTC)
- Thx Rob, I suspected as much. Please feel free to either fix them or to put an instance of
{{Mistake}}
or{{Questionable}}
template in place for each one. --prime mover (talk) 22:58, 16 April 2024 (UTC)