OFFSET
0,2
COMMENTS
Digits and formula given at Waldschmidt, p. 4.
REFERENCES
Mohammad K. Azarian, Problem 1218, Pi Mu Epsilon Journal, Vol. 13, No. 2, Spring 2010, p. 116. Solution published in Vol. 13, No. 3, Fall 2010, pp. 183-185.
L. B. W. Jolley, Summation of series, Dover Publications Inc. (New York), 1961, p. 46 (series n. 251).
A. J. Van Der Poorten, Effectively computable bounds for the solutions of certain Diophantine equations, Acta Arith., 33 (1977), pp. 195-207.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..10000
Michel Waldschmidt, Perfect Powers: Pillai's works and their developments, Aug 27, 2009.
FORMULA
Equals Sum_{n>=0} Sum_{m>=0} 1/((4*n+3)^(2*m+1)).
Equals Sum_{k>=1} 1/( (4*k-2)*(4*k-1)*(4*k) ). - Bruno Berselli, Mar 17 2014
EXAMPLE
0.0461254914187515000992143621808495764868961077417606...
1/(2*3*4) + 1/(6*7*8) + 1/(10*11*12) + 1/(14*15*16) + ... [Bruno Berselli, Mar 17 2014]
MAPLE
evalf[130]((Pi - 4*log(2))/8 ); # G. C. Greubel, Aug 11 2019
MATHEMATICA
Join[{0}, RealDigits[Pi/8-Log[2]/2, 10, 120][[1]]] (* Harvey P. Dale, Nov 13 2012 *)
PROG
(PARI) default(realprecision, 130); (Pi - 4*log(2))/8 \\ G. C. Greubel, Aug 11 2019
(Magma) SetDefaultRealField(RealField(130)); R:= RealField(); (Pi(R)-4*Log(2))/8; // G. C. Greubel, Aug 11 2019
(Sage) numerical_approx((pi-4*log(2))/8, digits=130) # G. C. Greubel, Aug 11 2019
CROSSREFS
KEYWORD
AUTHOR
Jonathan Vos Post, Aug 27 2009
EXTENSIONS
Normalized offset and leading zeros - R. J. Mathar, Sep 27 2009
STATUS
approved