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A030652 Continued fraction for Gamma(2/3). 4

%I #21 Aug 03 2024 13:25:23

%S 1,2,1,4,1,2,8,1,1,4,4,1,6,12,1,5,1,1,1,3,2,1,1,1,18,9,1,42,1,1,2,1,1,

%T 10,3,2,4,6,2,11,1,1,8,65,9,4,1,11,2,3,1,4,3,1,2,1,2,1,5,1,1,1,2,1,14,

%U 1,5,1,6,2,7,1,29,1,1,1,3,1,2,1,26,1,1,7,13,1,2,2,8,3,4,2,2,2

%N Continued fraction for Gamma(2/3).

%H Harry J. Smith, <a href="/A030652/b030652.txt">Table of n, a(n) for n = 0..4999</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>

%F Note that 3*GAMMA(1/3)*GAMMA(2/3) = 2*Pi*sqrt(3).

%e 1.354117939426400416945288028... = 1 + 1/(2 + 1/(1 + 1/(4 + 1/(1 + ...)))). - _Harry J. Smith_, May 14 2009

%t ContinuedFraction[Gamma[2/3],100] (* _Harvey P. Dale_, Sep 05 2021 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 5200); x=contfrac(gamma(2/3)); for (n=1, 5000, write("b030652.txt", n-1, " ", x[n])); } \\ _Harry J. Smith_, May 14 2009

%Y Cf. A030651, A073006 (decimal expansion).

%K nonn,cofr,changed

%O 0,2

%A Paolo Dominici (pl.dm(AT)libero.it)

%E Offset changed by _Andrew Howroyd_, Aug 03 2024

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Last modified August 14 19:51 EDT 2024. Contains 375167 sequences. (Running on oeis4.)