Integration produces "MeijerG::hdiv:" Error

Question

I am getting "Merijer::hdiv:" Error while evaluating the following integral.

η = 377; 

ncore = 1.4537;

V = {6,3,2,8};

\[Lambda] = 780*10^-9;

k = (2*Pi)/\[Lambda];

ρ = {1.7000000000000001*^-7, 5.*^-7, 1/1000000, 1/
          500000};

Umode = {1.42, 2.4048255576957724, 2.404825557695773, 
         2.4048255576957724};

Wmode = {0.266935298184825`, 3.5037278171663435`, 8.15193181742716`, 
         16.827522910778207`};

β = {8.206976900524202`*^6, 1.0676766940021148`*^7, 
   1.1460493452743163`*^7, 1.1648188685481489`*^7};

a1 = {-0.9716405362194648`, -0.7513937357444692`, \
-0.8094265682069952`, -0.8767301770575249`};

a2 = {0.02835946378053522`, 0.24860626425553078`, 0.1905734317930048`,
    0.12326982294247507`};

a3 = {-1.4936158488806575`, -2.299262374012871`, \
-2.2492698177690467`, -2.144294170304806`};

a4 = {0.25319207555967127`, -0.14963118700643552`, \
-0.12463490888452333`, -0.07214708515240298`};

a5 = {-0.483411020602892`, -0.8862342831689988`, \
-0.8612380050470866`, -0.8087501813149662`};

a6 = {-0.010204828277765476`, -0.41302809084387226`, \
-0.3880318127219601`, -0.3355439889898397`};

                             (*For Even Mode*)

f1 = Cos[ϕ];
g1 = -Sin[ϕ];

                             (*For Odd Mode*)

f2 = Sin[ϕ];
g2 = Cos[ϕ];

er1 = -((a1*BesselJ[0, Umode*r] + a2*BesselJ[2, Umode*r])/
      BesselJ[1, Umode])*f1;

er2 = -(Umode/
     Wmode)*((a1*BesselK[0, Wmode*r] - a2*BesselK[2, Wmode*r])/
    BesselK[1, Wmode])*f1;

eϕ1 = -((a1*BesselJ[0, Umode*r] - a2*BesselJ[2, Umode*r])/
      BesselJ[1, Umode])*g1;

eϕ2 = -(Umode/
     Wmode)*((a1*BesselK[0, Wmode*r] + a2*BesselK[2, Wmode*r])/
    BesselK[1, Wmode])*g1;

hr1 = (1/η)*((k*ncore^2)/β)*((a3*BesselJ[0, Umode*r] - 
       a4*BesselJ[2, Umode*r])/BesselJ[1, Umode])*g1;

hr2 = (1/η)*((k*ncore^2)/β)*(Umode/
     Wmode)*((a5*BesselK[0, Wmode*r] + a6*BesselK[2, Wmode*r])/
     BesselK[1, Wmode])*g1;

hϕ1 = -(1/η)*((k*
       ncore^2)/β)*((a3*BesselJ[0, Umode*r] + 
       a4*BesselJ[2, Umode*r])/BesselJ[1, Umode])*f1;

hϕ2 = - (1/η)*((k*ncore^2)/β)*(Umode/
     Wmode)*((a5*BesselK[0, Wmode*r] - a6*BesselK[2, Wmode*r])/
     BesselK[1, Wmode])*f1;

N1 = 0.5*Table[
   Integrate[(er1[[i]]*hϕ1[[i]] - 
       eϕ1[[i]]*hr1[[i]])*ρ[[i]]^2*r, {r, 0, 1}, {ϕ, 0,
      2*Pi}], {i, 1, Length[V]}]

N2 = 0.5*Table[
   Integrate[(er2[[i]]*hϕ2[[i]] - 
       eϕ2[[i]]*hr2[[i]])*ρ[[i]]^2*r, {r, 1, 2}, {ϕ, 0,
      2*Pi}], {i, 1, Length[V]}] 

1) The N2 integral generates "MeijerG::hdiv: "MeijerG[{{1.,1.5},{1.5}},{{-1.,1.,3.},{0.5,0.}},0.266935\ IntegrateImproperDumpnewx,0.5] does not exist. Arguments are not consistent. " error. The error is present only in first and second elements of N2. Please comment how to perform this integration.

Answer 1

The following parameters are not defined: k ncore^2, Length[V]. We put Length[V] = 4 then we have

 N1 = 0.5*Table[
   Integrate[(er1[[i]]*h\[Phi]1[[i]] - 
       e\[Phi]1[[i]]*hr1[[i]])*\[Rho][[i]]^2*r, {r, 0, 1}, {\[Phi], 0,
      2*Pi}], {i, 1, 4}]
N2 = 0.5*Table[
   Integrate[(er2[[i]]*h\[Phi]2[[i]] - 
       e\[Phi]2[[i]]*hr2[[i]])*\[Rho][[i]]^2*r, {r, 1, 2}, {\[Phi], 0,
      2*Pi}], {i, 1, 4}]

As a result, we get

{4.34209*10^-23 k ncore^2, 1.67433*10^-22 k ncore^2, 
 6.5924*10^-22 k ncore^2, 2.68594*10^-21 k ncore^2}
{5.42145*10^-23 k ncore^2, 4.23481*10^-24 k ncore^2, 
 2.0164*10^-24 k ncore^2, 1.07778*10^-24 k ncore^2}