如何在Mathematica中集成迭代函数

Question

我想计算像这样的积分https://i.stack.imgur.com/GHZiU.png

其中Micro是变量，并且

f0 = 1/(E^((w - \[Micro])/(K*T)) + 1);

Deri = -D[f0, w];

函数Coe（w）从迭代方法获得。 以一个简单的迭代函数为例： https : //i.stack.imgur.com/KBlKh.png就我而言，Coe（w）也依赖于“ w”，但方式复杂。 因此，Mathematica花费了很长时间来评估单元

在这里，我尝试以“ w”的形式对Coe进行数值积分，并在表外部更改Micro。

Table[
  {
   f0 = 1/(E^((w - \[Micro])/(K*T)) + 1);

   Deri = -D[f0, w];
   K = 8.61*10^-5;
   T = 300;
   S = NIntegrate[
     Coe*Deri*(w - \[Micro]), {w, \[Micro] - 50*K*T, \[Micro] + 
       50*K*T}];

   }
  , {\[Micro], -1, 1, 0.01}
  ];

我试图用“：=”定义一个函数Coe，如下所示

(*----------------------------------------DOS-------------------------------*)
Coe := Module[
   {
    n = 2, (*---Matrix Size---*)
    s = 3, (*---Max. iterative number---*)
    \[Eta] = 10^-4,
    \[Epsilon] = 0,
    t = 2.75
    },


   (*----------------Defining Matrices------------------------------------------------*)


   If[
    OddQ[n],

    L = (n - 1)/2;


    U = DiagonalMatrix[
      Flatten[{0, t, 0, 
        Table[{0, 0, 0, t, 0, 0, 0, t}, {i, 1, L}]}], -3];

    HH = DiagonalMatrix[
       Flatten[{\[Epsilon], \[Epsilon], \[Epsilon], \[Epsilon], \
\[Epsilon], \[Epsilon], 
         Table[{\[Epsilon], \[Epsilon], \[Epsilon], \[Epsilon], \
\[Epsilon], \[Epsilon], \[Epsilon], \[Epsilon]}, {i, 1, L}]}], 0] + 
      DiagonalMatrix[
       Flatten[{t, t, t, t, t, 
         Table[{0, t, t, t, 0, t, t, t}, {i, 1, L}]}], 1] +
      DiagonalMatrix[
       Flatten[{0, 0, 0, Table[{0, 0, 0, 0, t, 0, 0, 0}, {i, 1, L}]}],
        3] +
      DiagonalMatrix[
       Flatten[{0, 0, Table[{t, 0, 0, 0, 0, 0, 0, 0}, {i, 1, L}]}], 
       4] + 
      DiagonalMatrix[
       Flatten[{t, Table[{0, 0, 0, 0, 0, 0, 0, t}, {i, 1, L}]}], 5] + 
      If[n == 1, 0, 
       DiagonalMatrix[
        Flatten[Table[{0, 0, 0, t, 0, 0, 0, 0}, {i, 1, L}]], 6]
       ];

    Energy = (w + I*\[Eta])*
      DiagonalMatrix[
       Flatten[{1, 1, 1, 1, 1, 1, 
         Table[{1, 1, 1, 1, 1, 1, 1, 1}, {i, 1, L}]}], 0];

    ,
    L = n/2;


    U = DiagonalMatrix[
      Flatten[{0, t, 0, 0, 0, 0, t, 
        Table[{0, 0, 0, t, 0, 0, 0, t}, {i, 1, L - 1}]}], -3];

    HH = DiagonalMatrix[
       Flatten[{\[Epsilon], \[Epsilon], \[Epsilon], \[Epsilon], \
\[Epsilon], \[Epsilon], \[Epsilon], \[Epsilon], \[Epsilon], \
\[Epsilon], 
         Table[{\[Epsilon], \[Epsilon], \[Epsilon], \[Epsilon], \
\[Epsilon], \[Epsilon], \[Epsilon], \[Epsilon]}, {i, 1, L - 1}]}], 
       0] + DiagonalMatrix[
       Flatten[{t, t, t, t, t, 0, t, t, t, 
         Table[{0, t, t, t, 0, t, t, t}, {i, 1, L - 1}]}], 1] +

      DiagonalMatrix[
       Flatten[{0, 0, t, 0, 0, 0, 
         Table[{0, 0, 0, 0, 0, 0, 0, 0}, {i, 1, L - 1}]}], 4] +

      DiagonalMatrix[
       Flatten[{0, 0, 0, 0, 0, 0, 0, 
         Table[{t, 0, 0, 0, t, 0, 0, 0}, {i, 1, L - 1}]}], 3] +

      DiagonalMatrix[
       Flatten[{t, 0, 0, 0, 0, 
         Table[{0, 0, 0, t, 0, 0, 0, t}, {i, 1, L - 1}]}], 5] + 
      DiagonalMatrix[
       Flatten[{0, 0, 0, t, 
         Table[{0, 0, 0, 0, 0, 0, 0, 0}, {i, 1, L - 1}]}], 6];

    Energy = (w + I*\[Eta])*
      DiagonalMatrix[
       Flatten[{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
         Table[{1, 1, 1, 1, 1, 1, 1, 1}, {i, 1, L - 1}]}], 0];

    ];

   H = ConjugateTranspose[HH] + HH;
   (*----------------------------------------------------------------------------\
------*)


   (*---------------------------Iteration \
Coefficients-----------------------------------*)
   Subscript[a, 1] = 
    ConjugateTranspose[U].Inverse[Energy - H].ConjugateTranspose[U];
   \[Alpha] = ConjugateTranspose[U].Inverse[Energy - H].U;
   \[Beta] = U.Inverse[Energy - H].ConjugateTranspose[U];
   Subscript[b, 1] = U.Inverse[Energy - H].U;
   Subscript[c, 1] = Subscript[d, 1] = 0;
   (*---------------------------------------------------------------------------------*)
\



   (*--------------------------Iteration \
Start-----------------------------------------*)

   Table[
    Subscript[c, i] = 
     Subscript[c, i - 1] + 
      Subscript[a, 
       i - 1].Inverse[
        Energy - H - \[Alpha] - \[Beta] - Subscript[c, 
         i - 1]].Subscript[b, i - 1] + 
      Subscript[b, 
       i - 1].Inverse[
        Energy - H - \[Alpha] - \[Beta] - Subscript[c, 
         i - 1]].Subscript[a, i - 1];

    Subscript[a, i] = 
     Subscript[a, 
      i - 1].Inverse[
       Energy - H - \[Alpha] - \[Beta] - Subscript[c, 
        i - 1]].Subscript[a, i - 1];

    Subscript[b, i] = 
     Subscript[b, 
      i - 1].Inverse[
       Energy - H - \[Alpha] - \[Beta] - Subscript[c, 
        i - 1]].Subscript[b, i - 1];

    Ginf = Inverse[Energy - H - \[Alpha] - \[Beta] - Subscript[c, i]];

    , {i, 2, s}];

   (*-------------------------------------End------------------------------------------*)
\



   \[Rho] = -1/\[Pi] Im[Tr[Ginf]];
   (*--------------------------Return this--------------------------------------------\
*)
   \[Rho]

   ];

实际上，由于迭代函数Coe（w）已经在其他程序中运行，因此没有从集成中得到任何结果，这里的问题是如何集成此函数。