I have a problem about the plotting of a function which is defined as the power series
$$F(\eta)= \left[1+\frac{10.75}{\eta^{15/4}}+O\left(\frac{1}{\eta^{15/2}}\right)\right]^{-7/4} \biggr[1 + \frac{6G_4}{G_2\eta^{15/4}} +\frac{15 G_6}{G_2\eta^{15/2}}+\frac{28 G_8}{G_2\eta^{45/4}}+\frac{45 G_{10}}{G_2\eta^{15}} + \frac{66G_{12}}{G_2\eta^{75/4}} + \frac{91G_{14}}{G_2 \eta^{45/2}}+ O\left(\frac{1}{\eta^{105/4}}\right)\biggr]^{-1}$$
where $G_i$ are some known constant coefficients and the series as a function of $\eta$ is well-defined in the limit of $\eta\to+\infty$. The problem is that when considering this series as a normal function of $\eta$ and trying to plot it along the entire axis of this variable, the resulting plot produced by Mathematica goes to zero as $\eta$ approaches $0$. While the previous series has an evident divergence for $\eta\to0$ as seen if we stop the expansion to some low order
$$F(\eta)\approx 1-\left(\frac{75.25}{4}+\frac{6G_4}{G_2}\right)\frac{1}{\eta^{15/4}}+O\left(\frac{1}{\eta^{15/2}}\right)$$
In fact the plot that I got is
which I cannot really understand. For $\eta\to+\infty$ the function is correctly approaching $1$, but why for $\eta$ close to $3$ the function starts to decrease and it arrives to zero?
Here is my code
G2 = -1.8452283;
G4 = 8.33410;
G6 = -95.1884;
G8 = 1458.21;
G10 = -25889;
G12 = 5.02*^5;
G14 = -1.04*^7;
F[x_] := ((1 + 10.75/(x^(15/4)))^(-7/4))*((1 + (182*G14)/(
2*G2*x^(45/2)) + (132*G12)/(2*G2*x^(75/4)) + (56*G8)/(
2*G2*x^(45/4)) + (30*G6)/(2*G2*x^(15/2)) + (12*G4)/(
2*G2*x^(15/4)) + (90*G10)/(2*G2*x^15))^(-1))
Plot[F[x], {x, -3, 10}, PlotStyle -> ColorData[97][1]]