Zeta and Related Functions - 25.10 Zeros
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 25.10.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Z(t) = 2\sum_{n=1}^{m}\frac{\cos@{\vartheta(t)-t\ln@@{n}}}{n^{1/2}}+R(t)}
Z(t) = 2\sum_{n=1}^{m}\frac{\cos@{\vartheta(t)-t\ln@@{n}}}{n^{1/2}}+R(t) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Z(t) = 2*sum((cos(vartheta(t)- t*ln(n)))/((n)^(1/2)), n = 1..m)+ R(t)
|
Z[t] == 2*Sum[Divide[Cos[\[CurlyTheta][t]- t*Log[n]],(n)^(1/2)], {n, 1, m}, GenerateConditions->None]+ R[t]
|
Failure | Failure | Failed [300 / 300] 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}
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}
... skip entries to safe data |
Failed [300 / 300]
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]]]}
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]]]}
... skip entries to safe data |