(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 13.3' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 5696, 188] NotebookOptionsPosition[ 4998, 167] NotebookOutlinePosition[ 5392, 183] CellTagsIndexPosition[ 5349, 180] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"expression", " ", "=", " ", RowBox[{ FractionBox["37", "2"], "-", RowBox[{"30", RowBox[{"(", RowBox[{ RowBox[{"n", RowBox[{"(", RowBox[{ RowBox[{ FractionBox["q", RowBox[{"q", "-", "2"}]], RowBox[{"(", RowBox[{ RowBox[{"Log", "[", RowBox[{"2", ",", FractionBox["1", "\[Epsilon]"]}], "]"}], "+", "q"}], ")"}]}], "-", "1"}], ")"}]}], "+", "1"}], ")"}]}], "+", RowBox[{"18", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"n", RowBox[{"(", RowBox[{ RowBox[{ FractionBox["q", RowBox[{"q", "-", "2"}]], RowBox[{"(", RowBox[{ RowBox[{"Log", "[", RowBox[{"2", ",", FractionBox["1", "\[Epsilon]"]}], "]"}], "+", "q"}], ")"}]}], "-", "1"}], ")"}]}], "+", "1"}], ")"}], "^", "2"}]}], "+", RowBox[{"2", RowBox[{"(", RowBox[{"n", "-", "1"}], ")"}]}]}]}]], "Input", CellChangeTimes->{{3.906063908626438*^9, 3.906063993707685*^9}, { 3.9060640256280127`*^9, 3.906064111508772*^9}, {3.9060642340483294`*^9, 3.906064271834546*^9}}, CellLabel->"In[4]:=",ExpressionUUID->"ecf5c80d-975d-4892-88c6-001ebd7377b2"], Cell[BoxData[ RowBox[{ FractionBox["37", "2"], "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}]}], "-", RowBox[{"30", " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{"n", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", FractionBox[ RowBox[{"q", " ", RowBox[{"(", RowBox[{"q", "+", FractionBox[ RowBox[{"Log", "[", FractionBox["1", "\[Epsilon]"], "]"}], RowBox[{"Log", "[", "2", "]"}]]}], ")"}]}], RowBox[{ RowBox[{"-", "2"}], "+", "q"}]]}], ")"}]}]}], ")"}]}], "+", RowBox[{"18", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", RowBox[{"n", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", FractionBox[ RowBox[{"q", " ", RowBox[{"(", RowBox[{"q", "+", FractionBox[ RowBox[{"Log", "[", FractionBox["1", "\[Epsilon]"], "]"}], RowBox[{"Log", "[", "2", "]"}]]}], ")"}]}], RowBox[{ RowBox[{"-", "2"}], "+", "q"}]]}], ")"}]}]}], ")"}], "2"]}]}]], "Output", CellChangeTimes->{3.906064117039122*^9, 3.906064275522183*^9}, CellLabel->"Out[4]=",ExpressionUUID->"52c2006d-deec-42d1-a139-15ac762ba33a"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"Simplify", "[", "expression", "]"}]], "Input", CellChangeTimes->{{3.906064121728199*^9, 3.9060641326143093`*^9}, { 3.9060643199790373`*^9, 3.906064351806294*^9}}, CellLabel->"In[7]:=",ExpressionUUID->"02b903db-735e-48c0-b095-27572299b991"], Cell[BoxData[ RowBox[{ RowBox[{"-", FractionBox["23", "2"]}], "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}]}], "-", RowBox[{"30", " ", "n", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", FractionBox[ RowBox[{"q", " ", RowBox[{"(", RowBox[{"q", "+", FractionBox[ RowBox[{"Log", "[", FractionBox["1", "\[Epsilon]"], "]"}], RowBox[{"Log", "[", "2", "]"}]]}], ")"}]}], RowBox[{ RowBox[{"-", "2"}], "+", "q"}]]}], ")"}]}], "+", RowBox[{"18", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", RowBox[{"n", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", FractionBox[ RowBox[{"q", " ", RowBox[{"(", RowBox[{"q", "+", FractionBox[ RowBox[{"Log", "[", FractionBox["1", "\[Epsilon]"], "]"}], RowBox[{"Log", "[", "2", "]"}]]}], ")"}]}], RowBox[{ RowBox[{"-", "2"}], "+", "q"}]]}], ")"}]}]}], ")"}], "2"]}]}]], "Output", CellChangeTimes->{ 3.906064133111362*^9, 3.9060642814098177`*^9, {3.906064328656705*^9, 3.906064352272952*^9}}, CellLabel->"Out[7]=",ExpressionUUID->"7331ac0c-cf32-4dca-8f85-3dc9d8807a10"] }, Open ]] }, WindowSize->{808, 796}, WindowMargins->{{326, Automatic}, {30, Automatic}}, FrontEndVersion->"13.3 for Mac OS X ARM (64-bit) (July 24, 2023)", StyleDefinitions->"Default.nb", ExpressionUUID->"194f2364-7214-48fd-9fc9-64c50a78dc3f" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[580, 22, 1340, 41, 71, "Input",ExpressionUUID->"ecf5c80d-975d-4892-88c6-001ebd7377b2"], Cell[1923, 65, 1391, 44, 100, "Output",ExpressionUUID->"52c2006d-deec-42d1-a139-15ac762ba33a"] }, Open ]], Cell[CellGroupData[{ Cell[3351, 114, 267, 4, 30, "Input",ExpressionUUID->"02b903db-735e-48c0-b095-27572299b991"], Cell[3621, 120, 1361, 44, 123, "Output",ExpressionUUID->"7331ac0c-cf32-4dca-8f85-3dc9d8807a10"] }, Open ]] } ] *) (* End of internal cache information *)