From WM 11.1 CoordinateChartsData returns the following scale factor:
param = CoordinateChartData[{{"OblateSpheroidal", {\[FormalA]}},
"Euclidean", 3}, "StandardCoordinateNames"];
CoordinateChartData[{{"OblateSpheroidal", {a}}, "Euclidean", 3},
"ScaleFactors", param] /. x_String :> ToExpression[x] // Column
Where a is any constant and is the elliptical focus point. The code returns the following result:
\begin{array}{l} \frac{a \sqrt{\cos (2 \eta )+\cosh (2 \xi )}}{\sqrt{2}} \\ \frac{a \sqrt{\cos (2 \eta )+\cosh (2 \xi )}}{\sqrt{2}} \\ a \sin (\eta ) \cosh (\xi ) \\ \end{array}
But this result is different from what was published in the MathWorld Encyclopedia
Also contradicts what is published at Field Theory Handbook DOI: 10.1007/978-3-642-83243-7
Can anyone comment which is correct and if there might be a bug?
a
andparam
? $\endgroup$ – MarcoB Jul 24 '17 at 3:30