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Decimal expansion of log(1/2 + 1/sqrt(2))/sqrt(5).
1

%I #15 Sep 08 2022 08:45:38

%S 0,8,4,1,7,7,4,0,8,0,0,0,8,3,3,2,0,3,0,3,5,5,4,8,6,9,5,3,8,4,6,6,7,2,

%T 6,7,8,8,5,5,3,1,8,4,0,3,9,9,8,8,4,5,8,2,8,8,7,7,5,9,0,1,1,7,7,4,1,6,

%U 8,9,0,6,6,6,5,1,8,7,0,6,4,8,1,0,6,4,0,3,2,2,6,9,1

%N Decimal expansion of log(1/2 + 1/sqrt(2))/sqrt(5).

%C This is an erroneous version of A086466 produced by the Apelblat formula, which contains two typos.

%D Alexander Apelblat, Tables of Integrals and Series, Harri Deutsch, (1996), 4.1.42.

%H G. C. Greubel, <a href="/A145435/b145435.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals log(A014176/2)*A020762.

%e 0.084177408000833203035548695384667267885531840399884582887759..

%p 1/5*ln(1/2+1/2*2^(1/2))*5^(1/2) ;

%t Join[{0},RealDigits[Log[1/2+1/Sqrt[2] ]/Sqrt[5],10,120][[1]]] (* _Harvey P. Dale_, May 24 2016 *)

%o (PARI) default(realprecision, 100); 1/5*log(1/2+1/2*2^(1/2))*5^(1/2) \\ _G. C. Greubel_, Oct 02 2018

%o (Magma) SetDefaultRealField(RealField(100)); 1/5*Log(1/2+1/2*2^(1/2))*5^(1/2); // _G. C. Greubel_, Oct 02 2018

%Y Cf. A014176, A020762.

%K cons,easy,nonn

%O 0,2

%A _R. J. Mathar_, Feb 08 2009

%E Uncovered Apelblat errors. - _R. J. Mathar_, Mar 04 2009