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A342209
Decimal expansion of logarithmic mean of Pi and e.
0
2, 9, 2, 4, 8, 3, 3, 5, 4, 5, 2, 3, 7, 6, 9, 4, 8, 9, 9, 2, 7, 3, 3, 5, 9, 2, 2, 7, 6, 6, 1, 3, 5, 9, 4, 8, 2, 7, 8, 0, 3, 3, 8, 5, 3, 7, 6, 0, 2, 7, 4, 6, 8, 2, 2, 5, 4, 8, 2, 5, 9, 4, 8, 4, 9, 2, 8, 3, 2, 2, 9, 4, 5, 0, 4, 0, 1, 5, 8, 1, 6, 5, 8, 8, 5, 0, 3, 6, 9, 3, 5, 7, 8, 9, 5, 7, 6, 2, 9, 3, 9, 7, 4, 5, 0, 4, 0, 4
OFFSET
1,1
COMMENTS
The logarithmic mean of Pi and e lies between the arithmetic and geometric means of Pi and e.
LINKS
B. C. Carlson, The logarithmic mean, The American Mathematical Monthly, 79(6) 1972, pp. 615-618.
Wikipedia, Logarithmic mean.
FORMULA
Equals (Pi-e)/(log(Pi)-1).
EXAMPLE
2.9248335452376948992733592...
MATHEMATICA
RealDigits[(Pi - E)/(Log[Pi] - 1), 10, 100][[1]] (* Amiram Eldar, Mar 06 2021 *)
PROG
(PARI) (Pi-exp(1))/(log(Pi)-1)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Gleb Koloskov, Mar 05 2021
STATUS
approved