Timeline for Show how Mathematica defines a function
Current License: CC BY-SA 3.0
12 events
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| May 6, 2020 at 9:06 | history | edited | J. M.'s missing motivation♦ |
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| Apr 13, 2016 at 20:03 | comment | added | Yukterez | MathematicalFunctionData["JacobiAmplitude", "SeriesRepresentations"] works fine, thanks | |
| Apr 13, 2016 at 4:17 | vote | accept | Yukterez | ||
| Apr 12, 2016 at 18:19 | answer | added | Greg Hurst | timeline score: 16 | |
| Apr 12, 2016 at 18:01 | comment | added | kirma |
Have you looked at MathematicalFunctionData introduced in v10.3 (with ToEntity as demonstrated on its documentation)? I believe this is very much what you're looking for, and trying to extract this information from the way Mathematica actually works is probably a relatively futile effort in comparison.
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| Apr 12, 2016 at 18:01 | history | edited | Yukterez | CC BY-SA 3.0 |
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| Apr 12, 2016 at 18:00 | comment | added | J. M.'s missing motivation♦ |
4. Since a good amount of JacobiAmplitude[] is implemented as top-level code, PrintDefinitions[] from the GeneralUtilities` package can be revealing.
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| Apr 12, 2016 at 17:57 | history | edited | J. M.'s missing motivation♦ |
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| Apr 12, 2016 at 17:57 | comment | added | J. M.'s missing motivation♦ |
1. Using the integral definition directly for the complete elliptic integral is not the most efficient way for numerical evaluation; EllipticK[] is built-in, or if you must, ArithmeticGeometricMean[]. EllipticNomeQ[] is also built-in, and the most efficient algorithm also depends on the AGM. 2. The series for the Jacobian amplitude you are displaying has very limited numerical utility. 3. Note that Mathematica uses the parameter $m$ instead of the modulus $k$ as the second argument for the elliptic integrals and elliptic functions.
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| Apr 12, 2016 at 17:53 | history | edited | Yukterez | CC BY-SA 3.0 |
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| Apr 12, 2016 at 17:52 | history | edited | J. M.'s missing motivation♦ |
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| Apr 12, 2016 at 17:47 | history | asked | Yukterez | CC BY-SA 3.0 |