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