Re: HypergeometricPFQ Question

• To: mathgroup at smc.vnet.net
• Subject: [mg19007] Re: [mg18971] HypergeometricPFQ Question
• From: BobHanlon at aol.com
• Date: Tue, 3 Aug 1999 13:44:45 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```\$Version

"4.0 for Power Macintosh (April 20, 1999)"

Series[ HypergeometricPFQ[{1/2}, {3/2, 2}, -t^2] , {t, 0, 2} ]

\!\(\*
InterpretationBox[
RowBox[{"1", "-", \(t\^2\/6\), "+",
InterpretationBox[\(O[t]\^3\),
SeriesData[ t, 0, {}, 0, 3, 1]]}],
SeriesData[ t, 0, {1, 0,
Rational[ -1, 6]}, 0, 3, 1]]\)

However, back to the question of (0,0,1)

This is the partial derivative with respect to the third variable.
The position of the "1" tells you which for which variable the partial
derivative is taken. For example, look at

D[f[x, y, z], #] & /@ {x, y, z}

\!\(\*
RowBox[{"{",
RowBox[{
RowBox[{
SuperscriptBox["f",
TagBox[\((1, 0, 0)\),
Derivative],
MultilineFunction->None], "[", \(x, y, z\), "]"}], ",",
RowBox[{
SuperscriptBox["f",
TagBox[\((0, 1, 0)\),
Derivative],
MultilineFunction->None], "[", \(x, y, z\), "]"}], ",",
RowBox[{
SuperscriptBox["f",
TagBox[\((0, 0, 1)\),
Derivative],
MultilineFunction->None], "[", \(x, y, z\), "]"}]}], "}"}]\)

InputForm[%]

{Derivative[1, 0, 0][f][x, y, z], Derivative[0, 1, 0][f][x,
y, z], Derivative[0, 0, 1][f][x, y, z]}

In general, if you see a notation that is unfamiliar, try looking at the
InputForm. It is often clearer as to what function Mathematica is
using and how to get Help.

Bob Hanlon

In a message dated 7/30/99 7:50:02 AM, mjlee at postech.ac.kr writes:

>    ------------------------------------------------------------------
>     In[3]:= Series[ HypergeometricPFQ[{1/2},{3/2,2},-t^2] , {t,0,2} ]
>
>     gives
>                                  (0,0,1)  1    3          2       3
>     Out[4]= 1 - HypergeometricPFQ       [{-}, {-, 2}, 0] t  + O[t]
>                                           2    2
>     ------------------------------------------------------------------
>
>     What does (0,0,1) mean?
>     The Mathematica Book does not have any explanation.
>

```

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