How could I expand this equation (0.837 + x^0.5 + x)^4.870
Neither
Expand[(0.837 + x^0.5 + x)^4.870]
nor
Series[(0.837 + x^0.5 + x)^4.870, {x, 0, 6}]
work.
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It very strongly depends upon the answer to the question, why do you want to make the expansion and what is the range of x? For this reason in addition to the answer of Artes in the comment above you might think of the following approach for 0<x<1. This makes a fit of your function to a cubic polynomial:
lst = Table[{x, (0.837 + x^0.5 + x)^4.870}, {x, 0, 1, 0.01}];
ft = Fit[lst, {x, x^2, x^3}, x];
Show[{
ListPlot[lst, PlotStyle -> Blue],
Plot[ft, {x, 0, 1}, PlotStyle -> Red]
}]
That is how the fit looks like:
The blue points is your function and the red line is the fit. If this is a satisfactory coincidence, your expansion (or better to say, your approximation) is:
ft
(* 26.173 x + 20.6356 x^2 + 113.437 x^3 *)
answered Apr 29 '14 at 12:09
Series[(0.837 + x^(1/2) + x)^4.870 , {x, 0, 6}]i.e. switchx^0.5tox^(1/2)or simplySeries[(0.837 + x^0.5 + x)^4.870 // Rationalize, {x, 0, 6}]$\endgroup$ – Artes Apr 27 '14 at 16:09