Pi+e

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It is not known whether pi+e or pi-e are rational or irrational. In fact, there is no pair of nonzero integers $\scriptstyle m\,$ and $\scriptstyle n\,$ for which it is known whether $\scriptstyle m\pi +ne\,$ is rational or irrational. Moreover, it is not known whether the set $\scriptstyle \{\pi ,\,e\}\,$ is algebraically independent over $\scriptstyle \mathbb {Q} \,$.

Decimal expansion of pi+e

The decimal expansion of pi+e is

$\pi +e=5.859874482048838473822930854632165381954416493075065395941912220031893\ldots \,$

A059742 Decimal expansion of e+pi.

{5, 8, 5, 9, 8, 7, 4, 4, 8, 2, 0, 4, 8, 8, 3, 8, 4, 7, 3, 8, 2, 2, 9, 3, 0, 8, 5, 4, 6, 3, 2, 1, 6, 5, 3, 8, 1, 9, 5, 4, 4, 1, 6, 4, 9, 3, 0, 7, 5, 0, 6, 5, 3, 9, 5, 9, 4, 1, 9, 1, 2, 2, 2, 0, 0, 3, 1, 8, 9, 3, 0, 3, 6, 6, 3, 9, 7, 5, ...}

Continued fraction expansion of pi+e

The simple continued fraction expansion of pi+e is

$\pi +e=5~+~{\cfrac {1}{1+{\cfrac {1}{6+{\cfrac {1}{7+{\cfrac {1}{3+{\cfrac {1}{21+{\cfrac {1}{2+{\cfrac {1}{1+{\cfrac {1}{2+{\cfrac {1}{\ddots }}}}}}}}}}}}}}}}}}\,$

A058651 Continued fraction for pi+e.

{5, 1, 6, 7, 3, 21, 2, 1, 2, 2, 1, 1, 2, 3, 3, 2, 5, 2, 1, 1, 1, 1, 3, 1, 8, 4, 4, 1, 1, 1, 1, 8, 1, 4, 1, 5, 1, 1, 1, 2, 4, 3, 2, 1, 1, 2, 1, 10, 1, 4, 1, 2, 1, 12, 1, 8, 2, 7, 39, 365, 2, 15, 2, 25, 1, 2, 5, 3, 3, 9, 3, 1, 1, 9, ...}

See also

• pi+e
• pi-e
• pi*e
• pi/e
• pi^e
• e^pi (Gelfond's constant)