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D[f,x] vs f'[x]
*To*: mathgroup at smc.vnet.net
*Subject*: [mg7682] D[f,x] vs f'[x]
*From*: Gianluca Gorni <gorni at dimi.uniud.it>
*Date*: Sun, 29 Jun 1997 22:17:17 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
I have stumbled into a marked difference between
the derivation by D[] and the derivation as f',
that I don't quite understand.
Mathematica 3.0 Kernel for Power Macintosh
Let f be an infinite sum, which has a closed form:
In[1]:= f=Sum[x^n/(4n^2+4n+2),{n,0,Infinity}]//Simplify
1 I 1 I 3 I
Out[1]= (- + -) (-I HypergeometricPFQ[{- - -, 1}, {- - -}, x] +
4 4 2 2 2 2
1 I 3 I
> HypergeometricPFQ[{- + -, 1}, {- + -}, x])
2 2 2 2
The derivative is no problem:
In[2]:= D[f,x]//Simplify
I 1 I 3 I
Out[2]= (- (HypergeometricPFQ[{- - -, 1}, {- - -}, x] -
4 2 2 2 2
1 I 3 I
> HypergeometricPFQ[{- + -, 1}, {- + -}, x])) / x
2 2 2 2
However, if I define a function g[x] by that sum, using immediate
assignment (= instead of :=),
In[3]:= g[x_]=Sum[x^n/(4n^2+4n+2),{n,0,Infinity}]//Simplify
1 I 1 I 3 I
Out[3]= (- + -) (-I HypergeometricPFQ[{- - -, 1}, {- - -}, x] +
4 4 2 2 2 2
1 I 3 I
> HypergeometricPFQ[{- + -, 1}, {- + -}, x])
2 2 2 2
then the derivative g'[x] is Indeterminate!
In[4]:= g'[x]
Infinity::indet:
1 2 I 5 I
(-(-) - ---) Sqrt[5] ? Sign[Gamma[- - -]]
5 5 2 2
Indeterminate expression (-----------------------------------------) +
3 I
Sign[Gamma[- - -]]
2 2
<<1>> encountered.
Out[4]= Indeterminate
I am stumped. Is there a simple explanation?
Gianluca Gorni
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Gianluca Gorni
Universita` di Udine
Dipartimento di Matematica e Informatica
via delle Scienze 208
I-33100 Udine UD
Italy
Ph.:(39) (432) 558422 Fax:(39) (432) 558499
mailto:gorni at dimi.uniud.it
http://www.dimi.uniud.it
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