View source for 25.10

{{DISPLAYTITLE:Zeta and Related Functions - 25.10 Zeros}}

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| [https://dlmf.nist.gov/25.10.E3 25.10.E3] || [[Item:Q7673|<math>Z(t) = 2\sum_{n=1}^{m}\frac{\cos@{\vartheta(t)-t\ln@@{n}}}{n^{1/2}}+R(t)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>Z(t) = 2\sum_{n=1}^{m}\frac{\cos@{\vartheta(t)-t\ln@@{n}}}{n^{1/2}}+R(t)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Z(t) = 2*sum((cos(vartheta(t)- t*ln(n)))/((n)^(1/2)), n = 1..m)+ R(t)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Z[t] == 2*Sum[Divide[Cos[\[CurlyTheta][t]- t*Log[n]],(n)^(1/2)], {n, 1, m}, GenerateConditions->None]+ R[t]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.6950521340+1.584276130*I
Test Values: {R = 1/2*3^(1/2)+1/2*I, Z = 1/2*3^(1/2)+1/2*I, t = -3/2, vartheta = 1/2*3^(1/2)+1/2*I, m = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.464793153+1.882475916*I
Test Values: {R = 1/2*3^(1/2)+1/2*I, Z = 1/2*3^(1/2)+1/2*I, t = -3/2, vartheta = 1/2*3^(1/2)+1/2*I, m = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.6950521348622749, 1.5842761296673835]
Test Values: {Rule[m, 1], Rule[R, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[t, -1.5], Rule[Z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϑ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.4647931552284597, 1.8824759153846262]
Test Values: {Rule[m, 2], Rule[R, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[t, -1.5], Rule[Z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϑ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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