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A014538 Continued fraction for Catalan's constant 1 - 1/9 + 1/25 - 1/49 + 1/81 - ... 11

%I

%S 0,1,10,1,8,1,88,4,1,1,7,22,1,2,3,26,1,11,1,10,1,9,3,1,1,1,1,1,1,2,2,

%T 1,11,1,1,1,6,1,12,1,4,7,1,1,2,5,1,5,9,1,1,1,1,33,4,1,1,3,5,3,2,1,2,1,

%U 2,1,7,6,3,1,3,3,1,1,2,1,14,1,4,4,1,2,4,1,17,4,1,14,1,1,1,12,1

%N Continued fraction for Catalan's constant 1 - 1/9 + 1/25 - 1/49 + 1/81 - ...

%C First 4,851,389,025 terms computed by _Eric W. Weisstein_, Aug 07 2013.

%H Harry J. Smith, <a href="/A014538/b014538.txt">Table of n, a(n) for n = 0..20000</a>

%H G. J. Fee, <a href="http://dx.doi.org/10.1145/96877.96917">Computation of Catalan's constant using Ramanujan's formula</a>, in Proc. Internat. Symposium on Symbolic and Algebraic Computation (ISSAC '90). 1990, pp. 157-160.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CatalansConstantContinuedFraction.html">Catalan's Constant Continued Fraction</a>

%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>

%e C = 0.91596559417721901505... = 0 + 1/(1 + 1/(10 + 1/(1 + 1/(8 + ...))))

%t ContinuedFraction[Catalan, 100] (* _G. C. Greubel_, Aug 23 2018 *)

%o (PARI) default(realprecision, 100); contfrac(Catalan) \\ _G. C. Greubel_, Aug 23 2018

%o (MAGMA) R:= RealField(100); ContinuedFraction(Catalan(R)); // _G. C. Greubel_, Aug 23 2018

%Y Cf. A006752 (decimal expansion of Catalan's constant).

%Y Cf. A099789 (high water marks), A099790 (positions of high water marks).

%Y Cf. A006752, A104338, A153069, A153070, A054543, A118323. - _Stuart Clary_, Dec 17 2008

%K nonn,cofr

%O 0,3

%A _Eric W. Weisstein_

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Last modified April 21 13:43 EDT 2021. Contains 343153 sequences. (Running on oeis4.)