Editing Experimental mathematics (section)

== Plausible but false examples ==
{{main| mathematical coincidence}}

Some plausible relations hold to a high degree of accuracy, but are still not true. One example is:

:<math>
\int_{0}^{\infty}\cos(2x)\prod_{n=1}^{\infty}\cos\left(\frac{x}{n}\right)\mathrm{d}x = \frac{\pi}{8}.</math>

The two sides of this expression actually differ after the 42nd decimal place.<ref name=bailey>David H. Bailey and Jonathan M. Borwein, [http://crd.lbl.gov/~dhbailey/dhbpapers/math-future.pdf Future Prospects for Computer-Assisted Mathematics] {{Webarchive|url=https://web.archive.org/web/20110720013038/http://crd.lbl.gov/~dhbailey/dhbpapers/math-future.pdf |date=2011-07-20 }}, December 2005</ref>

Another example is that the maximum [[Height of a polynomial|height]] (maximum absolute value of coefficients) of all the factors of ''x''<sup>''n''</sup> − 1 appears to be the same as the height of the ''n''th [[cyclotomic polynomial]]. This was shown by computer to be true for ''n'' < 10000 and was expected to be true for all ''n''. However, a larger computer search showed that this equality fails to hold for ''n'' = 14235, when the height of the ''n''th cyclotomic polynomial is 2, but maximum height of the factors is 3.<ref>The height of Φ<sub>4745</sub> is 3 and 14235 = 3 x 4745. See Sloane sequences {{OEIS2C|id=A137979}} and {{OEIS2C|id=A160338}}.</ref>