Error Solving numerical integral

Questions
, ,
1

Hello everybody,

I’m trying to calculate an integral but it doesn’t give a numerical result. Which mistake did I do?
Any help would be appreciated!
Thanks

\[Mu]0 = 4*\[Pi]*10^-7;
\[Rho]max = 0.22;
q = {1};
i = 1;
j = 1;
n = {1};
aa = 0.130;
m = 1;
k = m;
Sq[\[Rho]_, i_] := (Sin[(Indexed[q, i]*\[Pi]*\[Rho])/\[Rho]max]);

dSq[\[Rho]_, 
   i_] := (Indexed[q, 
      i]*\[Pi]/\[Rho]max)*(Cos[(Indexed[q, 
         i]*\[Pi]*\[Rho])/\[Rho]max]);
\[Alpha][\[Rho]_] := ArcTan[\[Rho]/aa];


pn[\[Alpha]_, 
   j_] := (N[LegendreP[Indexed[n, j], m, Cos[\[Alpha][\[Rho]]]], 20]);

f[\[Rho]_] := (\[Rho]/ArcTan[\[Rho]/aa]);

Cnm[j_, f_] := ((Indexed[n, j] - m)!/(Indexed[n, j] + 
        m)!)*(1/(f[\[Rho]])^(Indexed[n, j] + 2));


pn1[\[Alpha]_, 
   j_] := (N[LegendreP[Indexed[n, j] + 1, m, Cos[\[Alpha][\[Rho]]]], 
    20]);

Cn\[Rho][pn_, \[Alpha]_] := (m*(pn[\[Alpha], j]/
      Sin[\[Alpha][\[Rho]]]));

Cnm\[Psi][j_, pn1_, 
   pn_, \[Alpha]_] := ((1/
      Sin[\[Alpha][\[Rho]]])*((Indexed[n, j] + 1)*
       pn[j, \[Alpha]] - (Indexed[n, j] - m + 1)*
       Cos[\[Alpha][\[Rho]]]*pn1[j, \[Alpha]]));
DD1 = Integrate[(\[Rho]*
    Cnm[j, 
     f] (Cn\[Rho][pn, \[Alpha]]*(k/\[Rho])*Sq[\[Rho], i] - 
      Cnm\[Psi][j, pn1, pn, \[Alpha]]*
       D[Sq[\[Rho], i], \[Rho]])), {\[Rho], 0, 0.1}]
2

Sometimes you write pn, pn1 and some others Pn, Pn1: if they mean the same, use the same capitalization. Then you must give a value to k and \[Alpha].

3

Hi Gianluca, thanks for the comment. There are two functions, pn and pn1. Alpha is a function of \rho. I’ve updated the script up there but still I cannot get the result.

4

This version gives a number:

\[Mu]0 = 4*\[Pi]*10^-7;
\[Rho]max = 0.22;
aa = 0.130;
Sq[\[Rho]_, i_] := (Sin[(Indexed[q, i]*\[Pi]*\[Rho])/\[Rho]max]);
dSq[\[Rho]_, 
   i_] := (Indexed[q, 
      i]*\[Pi]/\[Rho]max)*(Cos[(Indexed[q, 
         i]*\[Pi]*\[Rho])/\[Rho]max]);
\[Alpha][\[Rho]_] := ArcTan[\[Rho]/aa];
pn[j_] := (N[LegendreP[Indexed[n, j], m, Cos[\[Alpha][\[Rho]]]], 
    20]);
f[\[Rho]_] := (\[Rho]/ArcTan[\[Rho]/aa]);
Cnm[j_, f_] := ((Indexed[n, j] - m)!/(Indexed[n, j] + 
        m)!)*(1/(f[\[Rho]])^(Indexed[n, j] + 2));
pn1[\[Alpha]_, 
   j_] := (N[LegendreP[Indexed[n, j] + 1, m, Cos[\[Alpha][\[Rho]]]], 
    20]);
Cn\[Rho][
   pn_, \[Alpha]_] := (m*(pn[\[Alpha], j]/Sin[\[Alpha][\[Rho]]]));
Cnm\[Psi][j_, pn1_, 
   pn_, \[Alpha]_] := ((1/
      Sin[\[Alpha][\[Rho]]])*((Indexed[n, j] + 1)*
       pn[\[Alpha], j] - (Indexed[n, j] - m + 1)*
       Cos[\[Alpha][\[Rho]]]*pn1[\[Alpha], j]));
With[{q = {1}, i = 1, j = 1, n = {1}, m = 1, k = 1},
 NIntegrate[(\[Rho]*
    Cnm[j, 
     f] (Cn\[Rho][pn, \[Alpha]]*(k/\[Rho])*Sq[\[Rho], i] - 
      Cnm\[Psi][j, pn1, pn, \[Alpha]]*
       D[Sq[\[Rho], i], \[Rho]])), {\[Rho], 0, 0.1}]]

but it may not be what you are after. Your code is very difficult to read because you use the same symbols for both constants and variables, values and functions.

5

Sorry, I made a mistake, here is the correct code:

\[Mu]0 = 4*\[Pi]*10^-7;
\[Rho]max = 0.22;
aa = 0.130;
Sq[\[Rho]_, i_] := (Sin[(Indexed[q, i]*\[Pi]*\[Rho])/\[Rho]max]);
dSq[\[Rho]_, 
   i_] := (Indexed[q, 
      i]*\[Pi]/\[Rho]max)*(Cos[(Indexed[q, 
         i]*\[Pi]*\[Rho])/\[Rho]max]);
\[Alpha][\[Rho]_] := ArcTan[\[Rho]/aa];
pn[\[Alpha]_, 
   j_] := (N[LegendreP[Indexed[n, j], m, Cos[\[Alpha][\[Rho]]]], 
    20]);
f[\[Rho]_] := (\[Rho]/ArcTan[\[Rho]/aa]);
Cnm[j_, f_] := ((Indexed[n, j] - m)!/(Indexed[n, j] + 
        m)!)*(1/(f[\[Rho]])^(Indexed[n, j] + 2));
pn1[\[Alpha]_, 
   j_] := (N[LegendreP[Indexed[n, j] + 1, m, Cos[\[Alpha][\[Rho]]]], 
    20]);
Cn\[Rho][
   pn_, \[Alpha]_] := (m*(pn[\[Alpha], j]/Sin[\[Alpha][\[Rho]]]));
Cnm\[Psi][j_, pn1_, 
   pn_, \[Alpha]_] := ((1/
      Sin[\[Alpha][\[Rho]]])*((Indexed[n, j] + 1)*
       pn[\[Alpha], j] - (Indexed[n, j] - m + 1)*
       Cos[\[Alpha][\[Rho]]]*pn1[\[Alpha], j]));
Block[{q = {1}, i = 1, j = 1, n = {1}, m = 1, k = 1}, 
 NIntegrate[(\[Rho]*
    Cnm[j, 
     f] (Cn\[Rho][pn, \[Alpha]]*(k/\[Rho])*Sq[\[Rho], i] - 
      Cnm\[Psi][j, pn1, pn, \[Alpha]]*
       D[Sq[\[Rho], i], \[Rho]])), {\[Rho], 0, 0.1}]]