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A114875 - OEIS
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 3.2 Final//EN"> <html> <head> <link rel="stylesheet" href="/styles.css"> <meta name="format-detection" content="telephone=no"> <meta http-equiv="content-type" content="text/html; charset=utf-8"> <meta name=viewport content="width=device-width, initial-scale=1"> <meta name="keywords" content="OEIS,integer sequences,Sloane" /> <title>A114875 - OEIS</title> <link rel="search" type="application/opensearchdescription+xml" title="OEIS" href="/oeis.xml"> <script> var myURL = "\/A114875" function redir() { var host = document.location.hostname; if(host != "oeis.org" && host != "127.0.0.1" && !/^([0-9.]+)$/.test(host) && host != "localhost" && host != "localhost.localdomain") { document.location = "https"+":"+"//"+"oeis"+".org/" + myURL; } } function sf() { if(document.location.pathname == "/" && document.f) document.f.q.focus(); } </script> </head> <body bgcolor=#ffffff onload="redir();sf()"> <div class=loginbar> <div class=login> <a href="/login?redirect=%2fA114875">login</a> </div> </div> <div class=center><div class=top> <center> <div class=donors> The OEIS is supported by <a href="http://oeisf.org/#DONATE">the many generous donors to the OEIS Foundation</a>. </div> <div class=banner> <a href="/"><img class=banner border="0" width="600" src="/banner2021.jpg" alt="A114875 - OEIS"></a> </div> </center> </div></div> <div class=center><div class=pagebody> <div class=searchbarcenter> <form name=f action="/search" method="GET"> <div class=searchbargreet> <div class=searchbar> <div class=searchq> <input class=searchbox maxLength=1024 name=q value="" title="Search Query"> </div> <div class=searchsubmit> <input type=submit value="Search" name=go> </div> <div class=hints> <span class=hints><a href="/hints.html">Hints</a></span> </div> </div> <div class=searchgreet> (Greetings from <a href="/welcome">The On-Line Encyclopedia of Integer Sequences</a>!) </div> </div> </form> </div> <div class=sequence> <div class=space1></div> <div class=line></div> <div class=seqhead> <div class=seqnumname> <div class=seqnum> A114875 </div> <div class=seqname> Decimal expansion of -zeta'(1/2). </div> </div> <div class=scorerefs> 4 </div> </div> <div> <div class=seqdatabox> <div class=seqdata>3, 9, 2, 2, 6, 4, 6, 1, 3, 9, 2, 0, 9, 1, 5, 1, 7, 2, 7, 4, 7, 1, 5, 3, 1, 4, 4, 6, 7, 1, 4, 5, 9, 9, 5, 1, 3, 7, 3, 0, 3, 2, 3, 9, 7, 1, 5, 0, 6, 5, 0, 5, 2, 0, 9, 5, 6, 8, 2, 9, 8, 4, 8, 5, 2, 5, 4, 7, 2, 0, 8, 0, 3, 1, 5, 0, 3, 3, 8, 2, 8, 4, 8, 8, 0, 6, 5, 0, 5, 2, 3, 1, 0, 4, 1, 4, 5, 6, 9, 1, 4, 0</div> <div class=seqdatalinks> (<a href="/A114875/list">list</a>; <a href="/A114875/constant">constant</a>; <a href="/A114875/graph">graph</a>; <a href="/search?q=A114875+-id:A114875">refs</a>; <a href="/A114875/listen">listen</a>; <a href="/history?seq=A114875">history</a>; <a href="/search?q=id:A114875&fmt=text">text</a>; <a href="/A114875/internal">internal format</a>) </div> </div> </div> <div class=entry> <div class=section> <div class=sectname>OFFSET</div> <div class=sectbody> <div class=sectline>1,1</div> </div> </div> <div class=section> <div class=sectname>LINKS</div> <div class=sectbody> <div class=sectline><a href="/A114875/b114875.txt">Table of n, a(n) for n=1..102.</a></div> <div class=sectline>B. K. Choudhury, <a href="https://doi.org/10.1098/rspa.1995.0096">The Riemann zeta-function and its derivatives</a>, Proc. R. Soc. Lond. A 445 (1995) 477, Table 3.</div> <div class=sectline>J. Sondow and E. W. Weisstein, <a href="https://mathworld.wolfram.com/RiemannZetaFunction.html">MathWorld: Riemann Zeta Function</a>.</div> </div> </div> <div class=section> <div class=sectname>FORMULA</div> <div class=sectbody> <div class=sectline>Equals ((2*gamma + Pi + 2*log(8*Pi))*zeta(1/2))/4, where gamma is Euler's constant (<a href="/A001620" title="Decimal expansion of Euler's constant (or the Euler-Mascheroni constant), gamma.">A001620</a>).</div> </div> </div> <div class=section> <div class=sectname>EXAMPLE</div> <div class=sectbody> <div class=sectline>3.92264613920915172747153144671459951373032397150650...</div> </div> </div> <div class=section> <div class=sectname>MAPLE</div> <div class=sectbody> <div class=sectline>Zeta(1, 1/2) ; evalf(%) ; # <a href="/wiki/User:R._J._Mathar">R. J. Mathar</a>, May 03 2021</div> </div> </div> <div class=section> <div class=sectname>MATHEMATICA</div> <div class=sectbody> <div class=sectline>RealDigits[-Zeta'[1/2], 10, 120][[1]] (* <a href="/wiki/User:Amiram_Eldar">Amiram Eldar</a>, Jun 15 2023 *)</div> </div> </div> <div class=section> <div class=sectname>PROG</div> <div class=sectbody> <div class=sectline>(PARI) -zeta'(1/2) \\ <a href="/wiki/User:Charles_R_Greathouse_IV">Charles R Greathouse IV</a>, Mar 28 2012</div> <div class=sectline>(PARI) -(2*Euler+Pi+2*log(8*Pi))*zeta(1/2)/4 \\ <a href="/wiki/User:Charles_R_Greathouse_IV">Charles R Greathouse IV</a>, Mar 28 2012</div> </div> </div> <div class=section> <div class=sectname>CROSSREFS</div> <div class=sectbody> <div class=sectline>Cf. <a href="/A001620" title="Decimal expansion of Euler's constant (or the Euler-Mascheroni constant), gamma.">A001620</a>, <a href="/A059750" title="Decimal expansion of zeta(1/2) (negated).">A059750</a>.</div> <div class=sectline>Sequence in context: <a href="/A229099" title="Decimal expansion of 1 - 6/Pi^2.">A229099</a> <a href="/A021259" title="Decimal expansion of 1/255.">A021259</a> <a href="/A194807" title="Decimal expansion of 1/(e-2).">A194807</a> * <a href="/A275371" title="Decimal expansion of the surface area of the convex hull of two orthogonal tangent disks.">A275371</a> <a href="/A225357" title="Decimal expansion of (4/7)*(43/57)^(4/3).">A225357</a> <a href="/A201664" title="Decimal expansion of least x satisfying 2*x^2 - 1 = csc(x) and 0<x<Pi.">A201664</a></div> <div class=sectline>Adjacent sequences: <a href="/A114872" title="Even numbers not representable as (p-1)p^k (where p is a prime and k>=0) in ascending order.">A114872</a> <a href="/A114873" title="Numbers representable in exactly one way as (p-1)p^k (where p is a prime and k>=0), in ascending order.">A114873</a> <a href="/A114874" title="Numbers representable in exactly two ways as (p-1)*p^e (where p is a prime and e >= 0) in ascending order.">A114874</a> * <a href="/A114876" title="Let d(1)=1 and d(n) = d(n-1)*n^(2n-2)*(2n-1)^(3-2n). Then a(n)=numerator(d(n)).">A114876</a> <a href="/A114877" title="Let d(1)=1 and d(n) = d(n-1)*n^(2n-2)*(2n-1)^(3-2n). Then a(n) = denominator(d(n)).">A114877</a> <a href="/A114878" title="a(n) = (1/15)*(3*Fibonacci(5*(n+1)) - 5*Fibonacci(4*(n+1))).">A114878</a></div> </div> </div> <div class=section> <div class=sectname>KEYWORD</div> <div class=sectbody> <div class=sectline><span title="a sequence of nonnegative numbers">nonn</span>,<span title="a decimal expansion of a number"><a href="/A114875/constant">cons</a></span>,<span title="edited within the last two weeks">changed</span></div> </div> </div> <div class=section> <div class=sectname>AUTHOR</div> <div class=sectbody> <div class=sectline><a href="/wiki/User:Eric_W._Weisstein">Eric W. Weisstein</a>, Jan 03 2006</div> </div> </div> <div class=section> <div class=sectname>STATUS</div> <div class=sectbody> <div class=sectline>approved</div> </div> </div> </div> <div class=space10></div> </div> </div></div> <p> <div class=footerpad></div> <div class=footer> <center> <div class=bottom> <div class=linksbar> <a href="/">Lookup</a> <a href="/wiki/Welcome"><font color="red">Welcome</font></a> <a href="/wiki/Main_Page"><font color="red">Wiki</font></a> <a href="/wiki/Special:RequestAccount">Register</a> <a href="/play.html">Music</a> <a href="/plot2.html">Plot 2</a> <a href="/demo1.html">Demos</a> <a href="/wiki/Index_to_OEIS">Index</a> <a href="/webcam">WebCam</a> <a href="/Submit.html">Contribute</a> <a href="/eishelp2.html">Format</a> <a href="/wiki/Style_Sheet">Style Sheet</a> <a href="/transforms.html">Transforms</a> <a href="/ol.html">Superseeker</a> <a href="/recent">Recents</a> </div> <div class=linksbar> <a href="/community.html">The OEIS Community</a> </div> <div class=linksbar> Maintained by <a href="http://oeisf.org">The OEIS Foundation Inc.</a> </div> <div class=dbinfo>Last modified February 26 21:11 EST 2025. Contains 381238 sequences.</div> <div class=legal> <a href="/wiki/Legal_Documents">License Agreements, Terms of Use, Privacy Policy</a> </div> </div> </center> </div> </body> </html>