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Let me come straight to the point: I want to solve transcendental equation. Before down voting the question, I would like to say that I have checked most of the other questions and I haven't found any solutions (if there are any please let me know). My code goes like this:

ClearAll["Global`*"]
epsilonpL[w_, k_] := (w - L)/(1.22 k);
lambdap[k_] := 0.25 k^2;
Gammap[k_] := BesselI[L, lambdap[k]] Exp[-lambdap[k]];
Zp[w_, k_] := I* Sqrt[\[Pi]] Exp[- (epsilonpL[w, k])^2] (1 + Erf[I*epsilonpL[w, k]]);
pt[w_, k_] := 1 + \!\(\*UnderoverscriptBox[\(\[Sum]\), \(L = \(-1\)\), \(1\)]\(\*FractionBox[\(25000  Gammap[k]\),SuperscriptBox[\(k\), \(2\)]] \((1 +\*FractionBox[\(w\), \(\(1.22\)  \(k\)\(\ \)\)] Zp[w, k])\)\)\);
epsiloniL[w_, k_] := (w - 8 L - 0.86 k )/(3.46 k);
lambdai[k_] := 0.03 k^2;
Gammai[k_] := BesselI[L, lambdai[k]] Exp[-lambdai[k]];
Zi[w_, k_] := I* Sqrt[\[Pi]] Exp[- (epsiloniL[w, k])^2] (1 + Erf[I* epsiloniL[w, k]]);
it[w_, k_] := \!\(\*UnderoverscriptBox[\(\[Sum]\), \(L = \(-1\)\), \(1\)]\(\*FractionBox[\(2000000  Gammai[k]\), \(8 \*SuperscriptBox[\(k\), \(2\)]\)] \((1 + \*FractionBox[\(w - \((0.86  k)\)\), \(3.46\ k\)] Zi[w, k])\)\)\);
epsilone[w_, k_] := (0.027 w)/k;
Ze[w_, k_] := 0.44 I Hypergeometric2F1[1, 6, 4,1/2 (1 - epsilone[w, k]/(I 1.414))];
et[w_, k_] := 5000000/k^2 (0.75 + w/(42 k ) Ze[w, k]);
dispersion[w_, k_] := pt[w, k] + it[w, k] + et[w, k]
fRe[w_, k_] := ComplexExpand[dispersion[w, k]]
Table[{k, (w /.FindRoot[fRe[w, k] == 0, {w, {1/10, 1, 1/10, 1, 2, 1/10, 1}}, 
  Method -> "Secant"])}, {k, 0.1, 1, 0.1}] // Quiet
Table[{k, (w /. FindRoot[fRe[w, k] == 0, {w, {1/10, 1, 1/10, 1, 2, 1/10, 1}}])}, {k, 0.1, 1, 0.1}] // Quiet
Table[{k, (w /. FindRoot[dispersion[w, k] == 0, {w, {1/10, 1, 1/10, 1, 2, 1/10, 1}}, 
  Method -> "Secant"])}, {k, 0.1, 1, 0.1}] // Quiet
Table[{k, (w /. FindRoot[dispersion[w, k] == 0, {w, {1/10, 1, 1/10, 1, 2, 1/10, 1}}])}, {k, 0.1, 1,0.1}] // Quiet

For this thanks to Mariusz Iwaniuk and if possible, I invite his attention to this problem
@Mariusz. Here L is variable that can go from -10 to 10, but for time being I had given only from -1 to 1. As you can see, I had tried to solve this equation in four different ways, and all the time I am getting different answers. Now in this scenario, I am faced with the problem that which one is correct one???

Any help will be greatly appreciated... Thanks in Advance

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  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – Kuba Jan 9 '18 at 21:23
  • $\begingroup$ @Kuba, i didn't know hot to move the conversation to chat. thanks.. $\endgroup$ – sreeraj t Jan 10 '18 at 4:55

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