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Creating a function for Series expansion and unable of plotting series

Cornel B.

Posted 1 year ago

Hello, Subscript[E, 1] = Series[E^x, {x, 0, 1}] // Normal Subscript[E, 2] = Series[E^x, {x, 0, 2}] // Normal Subscript[E, 3] = Series[E^x, {x, 0, 3}] // Normal Subscript[E, 4] = Series[E^x, {x, 0, 4}] // Normal Plot[{Subscript[E, 1], Subscript[E, 2], Subscript[E, 3], Subscript[E, 4]}, {x, 0, 5}, PlotLegends -> {Subscript[E, 1], Subscript[E, 2], Subscript[E, 3], Subscript[E, 4]}, GridLines -> Automatic] Test[n_] := Series[E^x, {x, 0, n}] // Normal Plot[{Test[1], Test[2], Test[3], Test[4]}, {x, 0, 5}, PlotLegends -> {Test[1], Test[2], Test[3], Test[4]}, GridLines -> Automatic] Mathematica 13.2 Notebook file attached. Thank you. Attachments: Untitled-3.nb

Hello,

Subscript[E, 1] = Series[E^x, {x, 0, 1}] // Normal
Subscript[E, 2] = Series[E^x, {x, 0, 2}] // Normal
Subscript[E, 3] = Series[E^x, {x, 0, 3}] // Normal
Subscript[E, 4] = Series[E^x, {x, 0, 4}] // Normal
Plot[{Subscript[E, 1], Subscript[E, 2], Subscript[E, 3], Subscript[E, 
  4]}, {x, 0, 5}, 
 PlotLegends -> {Subscript[E, 1], Subscript[E, 2], Subscript[E, 3], 
   Subscript[E, 4]}, GridLines -> Automatic]

enter image description here

Test[n_] := Series[E^x, {x, 0, n}] // Normal
Plot[{Test[1], Test[2], Test[3], Test[4]}, {x, 0, 5}, 
 PlotLegends -> {Test[1], Test[2], Test[3], Test[4]}, 
 GridLines -> Automatic]

enter image description here

Mathematica 13.2 Notebook file attached.

Thank you.

POSTED BY: Cornel B.

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Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 1 year ago

You have to use Evaluate: Plot[{Test[1], Test[2], Test[3], Test[4]}, {x, 0, 5}, PlotLegends -> {Test[1], Test[2], Test[3], Test[4]}, GridLines -> Automatic] The problem is that `Test[n_]` is defined with a delayed definition `Test[n_] :=` and the numerical values of `x` are replaced in Test[1] before its definition is applied. The expressions E_n were defined with immediate evaluation. It is indeed rather subtle.

POSTED BY: Gianluca Gorni

Cornel B.

Posted 1 year ago

Ok. Thank you. I think that's what you meant when you said to use Evaluate (in the code posted by you, Evaluate doesn't appear) Test[n_] := Series[E^x, {x, 0, n}] // Normal Plot[{Evaluate[Test[1]], Evaluate[Test[2]], Evaluate[Test[3]], Evaluate[Test[4]]}, {x, 0, 5}, PlotLegends -> {Test[1], Test[2], Test[3], Test[4]}, GridLines -> Automatic]

Ok. Thank you. I think that's what you meant when you said to use Evaluate (in the code posted by you, Evaluate doesn't appear)

Test[n_] := Series[E^x, {x, 0, n}] // Normal
Plot[{Evaluate[Test[1]], Evaluate[Test[2]], Evaluate[Test[3]], 
  Evaluate[Test[4]]}, {x, 0, 5}, 
 PlotLegends -> {Test[1], Test[2], Test[3], Test[4]}, 
 GridLines -> Automatic]

enter image description here