# Solution of transcendental equation

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

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