|
|
A335027
|
|
Decimal expansion of Pi*(e-1)/2.
|
|
1
|
|
|
2, 6, 9, 9, 0, 7, 0, 7, 8, 4, 5, 4, 1, 8, 8, 6, 9, 1, 3, 5, 0, 0, 4, 5, 3, 7, 4, 3, 1, 3, 3, 5, 3, 5, 8, 0, 5, 4, 1, 8, 8, 5, 9, 5, 6, 8, 1, 9, 5, 0, 0, 4, 5, 7, 0, 4, 5, 2, 3, 2, 8, 2, 6, 8, 9, 3, 5, 7, 0, 6, 1, 0, 2, 4, 3, 5, 5, 6, 0, 9, 0, 4, 4, 7, 2, 2, 6
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The value of an integral (see formula) first calculated by Cauchy in 1825 (with an error that was corrected in 1826).
This integral appears in the forward to Vălean's book, written by Paul J. Nahin.
|
|
LINKS
|
Edward Thomas Copson, An Introduction to the Theory of Functions of a Complex Variable, London, 1935, Oxford, 1972 edition, p. 153.
|
|
FORMULA
|
Equals Integral_{x=0..oo} (exp(cos(x)) * sin(sin(x))/x) * dx (Cauchy, 1825-26).
Equals Integral_{x=0..oo} (exp(cos(x)) * sin(x) * sin(sin(x))/x^2) * dx (Vălean, 2019).
|
|
EXAMPLE
|
2.69907078454188691350045374313353580541885956819500...
|
|
MATHEMATICA
|
RealDigits[Pi*(E-1)/2, 10, 100][[1]]
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|