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MathGroup Archive 1997

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Re: Mathematica, Assumptions and Abramowitz & Stegun

  • To: mathgroup at smc.vnet.net
  • Subject: [mg8573] Re: Mathematica, Assumptions and Abramowitz & Stegun
  • From: "Paul E Howland" <PEHOWLAND at dra.hmg.gb>
  • Date: Sun, 7 Sep 1997 22:12:57 -0400
  • Organization: Defence Research Agency
  • Sender: owner-wri-mathgroup at wolfram.com

 I apologise for my previous posting, in which I tried to attach a
Mathematica
notebook to my email message, using Netscape Communicator.  For some
reason the attachment appears impossible to decode, and so I'm now trying
to include the notebook as ASCII directly beneath this message, using
Microsoft Outlook Express.  If that fails, I think I'll give up!

Anyway, once again, the Assumptions option doesn't seem to produce results
along the lines of Abramowitz and Stegun.  Any ideas what's going on?

Paul

Notebook follows:

(***********************************************************************

                    Mathematica-Compatible Notebook

This notebook can be used on any computer system with Mathematica 3.0,
MathReader 3.0, or any compatible application. The data for the notebook
starts with the line of stars above.

To get the notebook into a Mathematica-compatible application, do one of
the following:

* Save the data starting with the line of stars above into a file
  with a name ending in .nb, then open the file inside the application;

* Copy the data starting with the line of stars above to the
  clipboard, then use the Paste menu command inside the application.

Data for notebooks contains only printable 7-bit ASCII and can be
sent directly in email or through ftp in text mode.  Newlines can be
CR, LF or CRLF (Unix, Macintosh or MS-DOS style).

NOTE: If you modify the data for this notebook not in a Mathematica-
compatible application, you must delete the line below containing the
word CacheID, otherwise Mathematica-compatible applications may try to
use invalid cache data.

For more information on notebooks and Mathematica-compatible
applications, contact Wolfram Research:
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  email: info at wolfram.com
  phone: +1-217-398-0700 (U.S.)

Notebook reader applications are available free of charge from
Wolfram Research.
***********************************************************************)

(*CacheID: 232*)


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NotebookFileLineBreakTest*)
(*NotebookOptionsPosition[      3573,        120]*)
(*NotebookOutlinePosition[      4221,        143]*)
(*  CellTagsIndexPosition[      4177,        139]*)
(*WindowFrame->Normal*)



Notebook[{

Cell[CellGroupData[{
Cell["See Abramowitz and Stegun, p.12, eqn 3.3.26", "Title"],

Cell[TextData[{
  "I don't know whether ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  " is right, or Abromowitz and Stegun, but they're different!\nAre some of
\
the later assumptions too much for ",
  StyleBox["Mathematica",
    FontSlant->"Italic"],
  "?  The second assumption looks simple enough though, but the result is \
still different."
}], "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Integrate[1/Sqrt[\((a + b\ x)\) \((c + d\ x)\)], \ x, \n
        Assumptions \[Rule] {b*d\  < 0}]\  // PowerExpand\)], "Input"],

Cell[BoxData[
    \(Log[
        2\ \ at \(a + b\ x\)\ \ at \(c + d\ x\) +
          \(b\ c + a\ d + 2\ b\ d\ x\)\/\(\ at b\ \ at d\)]\/\(\ at b\ \ at d\)\)],
  "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Integrate[1/Sqrt[\((a + b\ x)\) \((c + d\ x)\)], \ x, \n
        Assumptions \[Rule] {b > 0, d\  < 0}]\  // PowerExpand\)], "Input"],

Cell[BoxData[
    \(Log[
        2\ \ at \(a + b\ x\)\ \ at \(c + d\ x\) +
          \(b\ c + a\ d + 2\ b\ d\ x\)\/\(\ at b\ \ at d\)]\/\(\ at b\ \ at d\)\)],
  "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Integrate[1/Sqrt[\((a + b\ x)\) \((c + d\ x)\)], \ x, \n
        Assumptions \[Rule] {d \((ad - bc)\) < 0}]\  // PowerExpand\)],
  "Input"],

Cell[BoxData[
    \(Log[
        2\ \ at \(a + b\ x\)\ \ at \(c + d\ x\) +
          \(b\ c + a\ d + 2\ b\ d\ x\)\/\(\ at b\ \ at d\)]\/\(\ at b\ \ at d\)\)],
  "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Integrate[1/Sqrt[\((a + b\ x)\) \((c + d\ x)\)], \ x, \n
        Assumptions \[Rule] {d \((ad - bc)\) > 0}]\  // PowerExpand\)],
  "Input"],

Cell[BoxData[
    \(Log[
        2\ \ at \(a + b\ x\)\ \ at \(c + d\ x\) +
          \(b\ c + a\ d + 2\ b\ d\ x\)\/\(\ at b\ \ at d\)]\/\(\ at b\ \ at d\)\)],
  "Output"]
}, Open  ]]
}, Open  ]]
},
FrontEndVersion->"Microsoft Windows 3.0",
ScreenRectangle->{{0, 800}, {0, 571}},
WindowSize->{500, 464},
WindowMargins->{{0, Automatic}, {Automatic, 0}}
]


(***********************************************************************
Cached data follows.  If you edit this Notebook file directly, not using
Mathematica, you must remove the line containing CacheID at the top of
the file.  The cache data will then be recreated when you save this file
from within Mathematica.
***********************************************************************)

(*CellTagsOutline
CellTagsIndex->{}
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(*CellTagsIndex
CellTagsIndex->{}
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Notebook[{

Cell[CellGroupData[{
Cell[1731, 51, 60, 0, 150, "Title"],
Cell[1794, 53, 368, 10, 71, "Text"],

Cell[CellGroupData[{
Cell[2187, 67, 147, 2, 50, "Input"],
Cell[2337, 71, 154, 4, 63, "Output"]
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Cell[CellGroupData[{
Cell[2874, 93, 160, 3, 50, "Input"],
Cell[3037, 98, 154, 4, 63, "Output"]
}, Open  ]],

Cell[CellGroupData[{
Cell[3228, 107, 160, 3, 50, "Input"],
Cell[3391, 112, 154, 4, 63, "Output"]
}, Open  ]]
}, Open  ]]
}
]
*)




(***********************************************************************
End of Mathematica Notebook file.
***********************************************************************)






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