       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:= f=Sum[x^n/(4n^2+4n+2),{n,0,Infinity}]//Simplify

1   I                         1   I       3   I
Out= (- + -) (-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:= D[f,x]//Simplify

I                     1   I       3   I
Out= (- (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

In:= g[x_]=Sum[x^n/(4n^2+4n+2),{n,0,Infinity}]//Simplify

1   I                         1   I       3   I
Out= (- + -) (-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:= g'[x]

Infinity::indet:
1    2 I                       5   I
(-(-) - ---) Sqrt ? Sign[Gamma[- - -]]
5     5                        2   2
Indeterminate expression (-----------------------------------------) +
3   I
Sign[Gamma[- - -]]
2   2
<<1>> encountered.

Out= 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

```

• Prev by Date: Making command called HoldTemporary
• Next by Date: Re: Error in basic integrals
• Previous by thread: Making command called HoldTemporary
• Next by thread: Re: Error in basic integrals