Re: D vs. Derivative (2)

• To: mathgroup at smc.vnet.net
• Subject: [mg15697] Re: D vs. Derivative (2)
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Mon, 1 Feb 1999 14:54:16 -0500 (EST)
• References: <78pcjv\$d3r@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Gianluca
Two definitions of Derivative to avoid the problems that you found. They
would need to be extended to several variables and higher derivatives,
and checked out -  for example for clashes of variables.

With

h[x_] =HypergeometricPFQ[{I,1},{1+I},x];

we got

D[h[x],x]
-(1/((-1 + x)*x)*I*(1 -
HypergeometricPFQ[{I, 1}, {1 + I}, x] +
x*HypergeometricPFQ[{I, 1}, {1 + I}, x]))

but
h'
DirectedInfinity[((1/2 + I/2)*Sqrt[2]*
Sign[Gamma[2 + I]])/Sign[Gamma[1 + I]]] &

If we define

Derivative[1][fn_]:=
Function[
Evaluate[
Function[#,
Evaluate[D[fn[#],#]]
]&[Unique[x]][#]
]
]

then we get

h'
-(1/((-1 + #1)*#1)*I*
(1 - HypergeometricPFQ[{I, 1}, {1 + I},
#1] + HypergeometricPFQ[{I, 1},
{1 + I}, #1]*#1)) &

And with

Derivative[1][fn_]:=
Function[Evaluate[Module[{x},D[fn[x],x]/.x->#]]]

we get the same:

h'

-(1/((-1 + #1)*#1)*I*
(1 - HypergeometricPFQ[{I, 1}, {1 + I},
#1] + HypergeometricPFQ[{I, 1},
{1 + I}, #1]*#1)) &

Allan,

---------------------
Allan Hayes
Mathematica Training and Consulting
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

```

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