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*To*: mathgroup at yoda.physics.unc.edu*From*: rvk at blink.att.com*Date*: Tue, 27 Oct 92 14:58:38 EST

thanks to the more than two dozen people who responded to my inquiry about converting a series to a function. a few people asked me to pass on any responses. I'm attaching a few represetative ones. -r. kline rvk at blink.att.com ========================================================================== In[10]:= f = (Normal[Series[Sin[x],{x,0,5}]] /. x->#)& Out[10]= Normal[Series[Sin[x], {x, 0, 5}]] /. x -> #1 & In[11]:= f[x] 3 5 x x Out[11]= x - -- + --- 6 120 In[12]:= f[r] 3 5 r r Out[12]= r - -- + --- 6 120 ========================================================================== The transforming of general expressions into functions is something that I regularly accomplish with the following inelegant but quick solution. Say I have an exression called bob: In[1]:= bob = Normal[ Series[ Sin[x], {x,0,5} ] ] 3 5 x x Out[1]= x - -- + --- 6 120 Now turn that into a function: In[2]:= fun[z_]:=bob/.{x->z} It now has all of the properties of ordinary functions of arbitrary arguments: In[3]:= fun[alpha] 3 5 alpha alpha Out[3]= alpha - ------ + ------ 6 120 In[4]:= D[fun[alpha],alpha] 2 4 alpha alpha Out[4]= 1 - ------ + ------ 2 24 ========================================================================== In[1]:= a=Normal[Series[Sin[x],{x,0,5}]] Out[1]= 3 5 x x x - -- + --- 6 120 In[5]:= f[x_]:=a The definition of the function f is not exactly what you want. In[6]:= ??f Global`f f[x_] := a The reason is that ":=", or in FullForm SetDelayed[], has the attribute HoldAll , which means it does not evaluate it's arguments. In this example it means tha t "a" does not evaluate to the series with "x" in it. In[7]:= Attributes[SetDelayed] Out[7]= {HoldAll, Protected} You can force evaluation of the right hand side by the following definition: In[9]:= f1[x_] := Evaluate[ a ] Note that you now get the desired result. In[10]:= ??f1 Global`f1 f1[x_] := x - x^3/6 + x^5/120 Wanting to assign a function to c computed result occurs often. ========================================================================== You asked about a=Normal[Series[Sin[x],{x,0,5}]] and f[x_]:=a ... What you want instead of f[x_]:=a is f[x_]:=Release[a]. That should do it. ========================================================================== Suppose I create a series, using a=Normal[Series[Sin[x],{x,0,5}]] giving a = x - x^3/3! + x^5/5!. I now want to use a to create a function of x, which, functionally, is f[x_]:=a. Define a=Normal[Series[Sin[x],{x,0,5}]] // InputForm and then F[x_] := Evaluate[a] // N. ========================================================================== You need to understand the distinction between Set[ ] ("=") and SetDelayed[ ] (":="). With SetDelayed[ ] you form a rule with the *unevaluated* right hand side. So if you type f[x_] := a you get exactly what you typed in and since there is no "x" in "a" there is nothing for the pattern matcher to match. It doesn't work. If you type f[x_] = a the "a" first gets evaluated to x - x^3/3! + x^5/5! and the rule that you get is then f[x_] = x - x^3/6 + x^5/120. This rule will then work. ========================================================================== You need to do an immediate assignment: f[x_] = a (* NOT f[x_] := a *)