Just wanted to know whether Euler was correct in assuming the laws of a finite polynomial to hold true even for an infinite polynomial when he working was on the infinite sum

1+1/4+1/9+1/16 .........

Or in other words is Euler justified in expanding an infinite polynomial into product of infinite roots as he did with the sin x/x case

And is he justified in equating the co-efficientls of infinite polynomials.as far as I have seen funny things happen when we apply rules of finite series to infinite series.

So is the proof that Euler gave us rigorous or is there a more rigorous proof.

No vote yet

3 votes

×

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewestThere's a more rigorous proof involving Fourier series.

Log in to reply