Daniel-- Thank you for looking at this. First, with regard to the "pattern variable", in my Mathematica notebook I did type pand[r_]::= but on one screen I saw it seemed that it did not come across that way with copy and paste.

Second, when on line 238 I define pand1[r_] by copying line 235 (the text explicit literal output of Normal applied to xpand[k,r,5] with k=2) I get a desired actual function of r which I can evaluate on line 240 at r=.2 and get the numerical result.

However, when on line 234 I try to define the function pand[r_] by setting it to the alleged normal expression xpandN5[k,r] with k=2, I do not get a function of r that can be evaluated at r=.2 (line 236). Mathematica still thinks there's a series involved, even though Normal has been applied to the series.By rights pand[r] should no longer be a series, but a function of r.

Third, in your next to last line should xpand be pand? Otherwise how else can pand[.2] be defined? And wouldn't xpand as a function of one variable conflict with its definition above as a function of three variables?

Finally, I'm not yet up to using Module, but maybe that's what's needed to get Normal to work the way I expect? In that case U'll try harder. Thanks again, --Karl