cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A094691 Decimal expansion of -Integral_{x=0..1} (sqrt(x)/log(1-x)) dx.

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%I A094691 #33 Jan 14 2025 06:02:19
%S A094691 1,6,0,1,4,0,2,2,4,3,5,4,9,8,8,7,6,1,3,9,3,3,2,4,9,8,9,2,3,7,1,2,8,6,
%T A094691 0,5,6,6,7,2,4,1,0,8,9,9,3,1,4,1,6,5,4,5,3,2,7,3,1,1,4,8,7,1,0,4,5,7,
%U A094691 3,8,5,5,4,8,3,8,7,5,0,4,5,8,8,3,7,9,3,0,6,8
%N A094691 Decimal expansion of -Integral_{x=0..1} (sqrt(x)/log(1-x)) dx.
%H A094691 Simon Plouffe, <a href="https://web.archive.org/web/20080205202100/http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap103.html">-int(sqrt(x)/log(1-x),x=0..1)</a>.
%F A094691 Equals 5/3 - 2*Sum_{k>=1} abs(Sum_{j=1..k+1} (BernoulliB(j)*Stirling1(k, j-1))/j)/((2*k+3)*k!). - _Jean-François Alcover_, Apr 12 2013
%F A094691 Equals Integral_{x=0..1} beta(x+1,1/2) dx. - _Jean-Luc Marichal_, Sep 22 2020
%e A094691 1.601402243549887613933249892371286056672410899314165453273114871045738554838...
%t A094691 -NIntegrate[ Sqrt[x]/Log[1 - x], {x, 0, 1}, MaxRecursion -> 24, WorkingPrecision -> 98]
%t A094691 RealDigits[NIntegrate[Sqrt[x]/Log[1-x],{x,0,1},WorkingPrecision-> 120],10,120] [[1]] (* _Harvey P. Dale_, Apr 05 2019 *)
%o A094691 (PARI) -intnum(x=0, 1, sqrt(x)/log(1-x)) \\ _Michel Marcus_, Sep 23 2020
%K A094691 cons,nonn
%O A094691 1,2
%A A094691 _Robert G. Wilson v_, May 19 2004
%E A094691 Corrected and extended by _Harvey P. Dale_, Apr 05 2019