I'm trying to plot a parametric curve, but I only get a blank plot. I don't usually use mathematica, but my end user needs to be able to do this using that software, so I'm really struggling on syntax

ParametricPlot3D[{(2 - 2*ProductLog[[2*0.003*E]]^(Sqrt*(2*Pi)))*Sin[x]*Cos[y], (2 - 2*ProductLog[[2*0.003*E]]^(Sqrt*(2*Pi)))*Sin[x]*Sin[y], (2 - 2*ProductLog[[2*0.003*E]]^(Sqrt*(2*Pi)))*Cos[x]}, {x, 0.040893729329, 3.10069892426}, {y, ArcSin[0.0408823325378/Sin[x]], Pi - ArcSin[0.0408823325378/Sin[x]]}]

What am I doing wrong?

c= .003 I'm using this data: https://www.dropbox.com/scl/fi/4y5gi8z5d06kr4srwrtkr/SIparametricv2-revisions.docx?dl=0&rlkey=9nw4b7w3lergzt129wva8cpsr

Equations source Mathematica Input/Output

  • 1
    $\begingroup$ Capitalization matters (Sqrt, ArcSin, etc.), and as you've already seen with ProductLog, you should be using brackets ([]) instead of parentheses (()) for functions. It's also a good idea to link to the book/paper/whatever you're referring to when asking questions like these. $\endgroup$
    – J. M.'s torpor
    Feb 8 at 12:26
  • $\begingroup$ Please provide your Mathematica Code, this will increase the chance of a helpful answer! Mathematica functions usually atrat with a capital letter, change to Sqrt, Sin, Cos, ArcSin,Pi,... $\endgroup$ Feb 8 at 12:27
  • $\begingroup$ A[[n]] indexes Part n of an expression A, such as a vector, list, or array. A[n] calls the function A on the argument n. For example, ProductLog[[2*0.003*E]] should have single brackets instead of double ones. Bracket astigmatism is one of the pitfalls of Mathematica, at least for people like me. $\endgroup$
    – Michael E2
    Feb 9 at 15:57

You have a lot of trivial syntax mistakes. Most probably your question will be closed for this reason. Anyway, by correcting them we get a working code.

ParametricPlot3D[{(2 - 2*ProductLog[2*0.003*E]^(Sqrt[2*Pi]))*Sin[x]*
   Cos[y], (2 - 2*ProductLog[2*0.003*E]^(Sqrt[2*Pi]))*Sin[x]*
   Sin[y], (2 - 2*ProductLog[2*0.003*E]^(Sqrt[2*Pi]))*Cos[x]}, {x, 
  0.040893729329, 3.10069892426}, {y, ArcSin[0.0408823325378/Sin[x]], 
  Pi - ArcSin[0.0408823325378/Sin[x]]}]

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