I am quite new in Mathematica and I am trying to plot a linear term of a particular function in Mathematica. I have tried something like this:
TD = 200
Debye[x_] := 3 (x/TD)^3 NIntegrate[y^3/(Exp[y] - 1), {y, 0, TD/x}]
Fa[x_] := 8.6173324*10^(-5) x (9 *TD/(8 x) + 3 Log[1 - Exp[-TD/x]] -
Debye[x])
Series[Fa[x], {x, 0, 1}]
Actually I want to plot Fa[x] with the linear term expansion. It shows some error called
"NIntegrate::nlim: "y = 200./t is not a valid limit of integration"
However If I just simply plot Fa[x] (without the series syntax), it works. It seems I am missing something regarding the Series syntax. Could anyone please help me out?
Normal[]
to make the expression returned bySeries[]
work. $\endgroup$ – egwene sedai Feb 1 '16 at 14:50Series[]
needs a symbolic expression and here you have a numeric one. I thinkDebye[]
has a closed analytic expression, and you can work from there $\endgroup$ – egwene sedai Feb 1 '16 at 14:56Debye
as a function that only handles explicitly numeric input. This is done asDebye[x_?NumberQ]:=...
. (2) Makeser
into a function also restricted to explicit numeric input (and useNormal
, as was already noted by @egwenesedai):ser[x_?NumberQ] := Normal[Series[Fa[y], {y, 0, 1}]] /. y -> x
. First remember to clear the prior definitions:Clear[Debye,ser]
. $\endgroup$ – Daniel Lichtblau Feb 1 '16 at 15:39