A222171 Decimal expansion of Pi^2/24.

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

Offset: 0

Author

Jean-François Alcover, May 13 2013

Keywords

• nonn
• cons
• easy

Examples

			0.411233516712056609118103791661506297304737475301699609433889557342501867600...
		

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

• Index entries for transcendental numbers

Crossrefs

Cf. A000005, A013679, A111003, A072691, A078471, A369180.

Programs

Magma

pi:=Pi(RealField(110)); Reverse(Intseq(Floor(10^100*(pi)^2/24))); // Vincenzo Librandi, Sep 25 2015

Mathematica

RealDigits[Pi^2/24, 10, 100] // First

PARI

Pi^2/24 \\ Michel Marcus, Dec 10 2020

Formula

Equals Integral_{x=0..Pi/2} log(sec(x))/tan(x) dx.

Equals Sum_{k >= 1} 1/(2k)^2. - Geoffrey Critzer, Nov 02 2013

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

Equals Sum_{n>=1} A369180(n)/n^2. - Friedjof Tellkamp, Jan 23 2025

Extensions

Leading 0 term removed (to make offset correct) by Rick L. Shepherd, Jan 01 2014