(Redirected from E^pi-pi^e)
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It is not known whether
is
irrational or
rational. ([[e^pi|
]], known as
Gelfond's constant, is a
transcendental number. It is not known whether [[pi*e|
]], [[pi/e|
]], [[2^e|
]], [[pi^e|
]], [[pi^sqrt(2)|
]], [[log pi|
]],
Catalan's constant, or the
Euler–Mascheroni constant are irrational or rational.
[1][2][3])
Decimal expansion of e^pi−pi^e
The
decimal expansion of
is
giving the sequence of decimal digits (A063504)
- {6, 8, 1, 5, 3, 4, 9, 1, 4, 4, 1, 8, 2, 2, 3, 5, 3, 2, 3, 0, 1, 9, 3, 4, 1, 6, 3, 4, 0, 4, 8, 1, 2, 3, 5, 2, 6, 7, 6, 7, 9, 1, 1, 0, 8, 6, 0, 3, 5, 1, 9, 7, 4, 4, 2, 4, 2, 0, 4, 3, 8, 5, 5, 4, 5, 7, 4, 1, 6, 3, 1, 0, 2, 9, 1, 3, 3, ...}
Continued fraction expansion of e^pi−pi^e
The
simple continued fraction expansion of
is
giving the sequence of partial quotients (A063503)
- {0, 1, 2, 7, 7, 6, 2, 1, 6, 2, 5, 7, 1, 3, 1, 1, 6, 1, 1, 1, 1, 1, 2, 1, 11, 5, 6, 2, 1, 124, 1, 4, 2, 1, 1, 3, 18, 1, 1, 1, 1, 17, 1, 2, 10, 1, 1, 1, 2, 2, 2, 2, 3, 1, 2, 4, 84, 1, 1, 1, 4, 1, 1, 15, 2, 1, 1, 17, 1, 1, 8, 1, 1, ...}
See also
- [[pi+e| ]]
- [[pi−e| ]]
- [[pi*e| ]]
- [[pi/e| ]]
- [[pi^e| ]]
- [[e^pi| ]] (Gelfond's constant)
- [[e^pi−pi^e| ]]
- [[sqrt(pi*e/2)| ]]
Notes