|
|
A222171
|
|
Decimal expansion of Pi^2/24.
|
|
20
|
|
|
4, 1, 1, 2, 3, 3, 5, 1, 6, 7, 1, 2, 0, 5, 6, 6, 0, 9, 1, 1, 8, 1, 0, 3, 7, 9, 1, 6, 6, 1, 5, 0, 6, 2, 9, 7, 3, 0, 4, 7, 3, 7, 4, 7, 5, 3, 0, 1, 6, 9, 9, 6, 0, 9, 4, 3, 3, 8, 8, 9, 5, 5, 7, 3, 4, 2, 5, 0, 1, 8, 6, 7, 6, 0, 0, 8, 0, 0, 2, 1, 8, 4, 5, 8, 4, 0, 7, 2, 2, 5, 1, 5, 4, 9, 3, 9, 6, 7, 6, 3
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
REFERENCES
|
George Boros and Victor H. Moll, Irresistible integrals, Cambridge University Press, 2006, p. 242.
Ovidiu Furdui, Limits, Series, and Fractional Part Integrals: Problems in Mathematical Analysis, New York: Springer, 2013. See Problem 3.45, p. 158 and 199-200.
|
|
LINKS
|
|
|
FORMULA
|
Equals Integral_{x=0..Pi/2} log(sec(x))/tan(x) dx.
Equals (1/10) * Sum_{k>=1} d(k^2)/k^2, where d(k) is the number of divisors of k (A000005). - Amiram Eldar, Jun 27 2020
Equals Sum_{n >= 0} 1/((2*n+1)*(6*n+3)). - Peter Bala, Feb 02 2022
Equals Sum_{n>=0} ((-1)^n * (Sum_{k>=n+1} (-1)^k/k)^2) (Furdui, 2013). - Amiram Eldar, Mar 26 2022
|
|
EXAMPLE
|
0.411233516712056609118103791661506297304737475301699609433889557342501867600...
|
|
MATHEMATICA
|
RealDigits[Pi^2/24, 10, 100] // First
|
|
PROG
|
(Magma) pi:=Pi(RealField(110)); Reverse(Intseq(Floor(10^100*(pi)^2/24))); // Vincenzo Librandi, Sep 25 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Leading 0 term removed (to make offset correct) by Rick L. Shepherd, Jan 01 2014
|
|
STATUS
|
approved
|
|
|
|