Algebraic and Analytic Methods - 1.10 Functions of a Complex Variable
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 1.10.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\ln@{1+a_{n}(z)}| \leq M_{n}}
|\ln@{1+a_{n}(z)}| \leq M_{n} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n \geq N} | abs(ln(1 + a[n](z))) <= M[n]
|
Abs[Log[1 + Subscript[a, n][z]]] <= Subscript[M, n]
|
Failure | Failure | Failed [126 / 300] Result: .7588760888 <= -1.5
Test Values: {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = 1/2*3^(1/2)+1/2*I, n = 1}
Result: .7588760888 <= -1.5
Test Values: {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = 1/2*3^(1/2)+1/2*I, n = 2}
Result: .7588760888 <= -1.5
Test Values: {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = 1/2*3^(1/2)+1/2*I, n = 3}
Result: 1.465287519 <= -1.5
Test Values: {z = 1/2*3^(1/2)+1/2*I, M[n] = -1.5, a[n] = -1/2+1/2*I*3^(1/2), n = 1}
... skip entries to safe data |
Failed [246 / 300]
Result: LessEqual[0.7588760887069661, Complex[0.8660254037844387, 0.49999999999999994]]
Test Values: {Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[M, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: LessEqual[0.7588760887069661, Complex[0.8660254037844387, 0.49999999999999994]]
Test Values: {Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[M, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
... skip entries to safe data |
| 1.10.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{\infty}_{n=1}M_{n} < \infty}
\sum^{\infty}_{n=1}M_{n} < \infty |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(M[n](<)*infinity, n = 1..infinity) |
Sum[Subscript[M, n][<]*Infinity, {n, 1, Infinity}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.10.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle P(z) = \prod^{\infty}_{n=1}\left(1-\frac{z}{z_{n}}\right)e^{z/z_{n}}}
P(z) = \prod^{\infty}_{n=1}\left(1-\frac{z}{z_{n}}\right)e^{z/z_{n}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | P(z) = product((1 -(z)/(z[n]))*exp(z/z[n]), n = 1..infinity) |
P[z] == Product[(1 -Divide[z,Subscript[z, n]])*Exp[z/Subscript[z, n]], {n, 1, Infinity}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |