Spheroidal Wave Functions - 30.15 Signal Analysis
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 30.15.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acos@@{\sqrt{\mathrm{B}}}+\acos@@{\sqrt{\alpha}} = \acos@@{\sqrt{\Lambda_{0}}}}
\acos@@{\sqrt{\mathrm{B}}}+\acos@@{\sqrt{\alpha}} = \acos@@{\sqrt{\Lambda_{0}}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | arccos(sqrt(B))+ arccos(sqrt(alpha)) = arccos(sqrt(Lambda[0]))
|
ArcCos[Sqrt[B]]+ ArcCos[Sqrt[\[Alpha]]] == ArcCos[Sqrt[Subscript[\[CapitalLambda], 0]]]
|
Failure | Failure | Failed [300 / 300] Result: .6584789493*I
Test Values: {B = 1/2*3^(1/2)+1/2*I, Lambda = 1/2*3^(1/2)+1/2*I, alpha = 3/2, Lambda[0] = 1/2*3^(1/2)+1/2*I}
Result: -.6623382543+1.000904144*I
Test Values: {B = 1/2*3^(1/2)+1/2*I, Lambda = 1/2*3^(1/2)+1/2*I, alpha = 3/2, Lambda[0] = -1/2+1/2*I*3^(1/2)}
... skip entries to safe data |
Failed [300 / 300]
Result: Complex[0.0, 0.6584789484624083]
Test Values: {Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[Λ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[-0.6623382542357523, 1.0009041434383552]
Test Values: {Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Λ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[Λ, 0], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
... skip entries to safe data |
| 30.15.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathrm{B} = \left(\sqrt{\Lambda_{0}\alpha}+\sqrt{1-\Lambda_{0}}\sqrt{1-\alpha}\right)^{2}}
\mathrm{B} = \left(\sqrt{\Lambda_{0}\alpha}+\sqrt{1-\Lambda_{0}}\sqrt{1-\alpha}\right)^{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | B = (sqrt(Lambda[0]*alpha)+sqrt(1 - Lambda[0])*sqrt(1 - alpha))^(2) |
B == (Sqrt[Subscript[\[CapitalLambda], 0]*\[Alpha]]+Sqrt[1 - Subscript[\[CapitalLambda], 0]]*Sqrt[1 - \[Alpha]])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 30.15#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a = \sqrt{\frac{\alpha}{\Lambda_{0}}}}
a = \sqrt{\frac{\alpha}{\Lambda_{0}}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | a = sqrt((alpha)/(Lambda[0])) |
a == Sqrt[Divide[\[Alpha],Subscript[\[CapitalLambda], 0]]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 30.15#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b = \sqrt{\frac{1-\alpha}{1-\Lambda_{0}}}}
b = \sqrt{\frac{1-\alpha}{1-\Lambda_{0}}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | b = sqrt((1 - alpha)/(1 - Lambda[0])) |
b == Sqrt[Divide[1 - \[Alpha],1 - Subscript[\[CapitalLambda], 0]]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |