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A222183 Decimal expansion of Sum_{k >= 0} 1/(4*k+1)^2. 5

%I

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

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

%U 3,4,3,1,1,2,8,9,3,2,7,7,1,2,4,2,7,2,8

%N Decimal expansion of Sum_{k >= 0} 1/(4*k+1)^2.

%H Vincenzo Librandi, <a href="/A222183/b222183.txt">Table of n, a(n) for n = 1..5000</a>

%F Equals A006752/2 + A222068.

%F Equals -Integral_{x=0..1} log(x)/(1 - x^4) dx. - _Amiram Eldar_, Jul 17 2020

%e 1.074833072156694421204457444958451501344... = 1 + 1/25 + 1/81 + 1/169 + 1/289 + ...

%t RealDigits[Catalan/2 + Pi^2/16, 10, 90][[1]] (* or *) RealDigits[PolyGamma[1, 1/4]/16, 10, 90]

%o (PARI) (8*Catalan + Pi^2)/16 \\ _G. C. Greubel_, Aug 23 2018

%o (MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); (8*Catalan(R) + Pi(R)^2)/16; // _G. C. Greubel_, Aug 23 2018

%Y Cf. A006752, A222068.

%Y Cf. A013661, A111003, A214550.

%K nonn,cons

%O 1,3

%A _Bruno Berselli_, Feb 11 2013

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Last modified April 20 19:33 EDT 2021. Contains 343137 sequences. (Running on oeis4.)