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MathGroup Archive 1996

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Re: SeriesData

  • To: mathgroup at smc.vnet.net
  • Subject: [mg5558] Re: SeriesData
  • From: wilson figueroa <wfigueroa at mosquito.com>
  • Date: Thu, 19 Dec 1996 01:02:45 -0500
  • Organization: Mosquito Net, Inc.
  • Sender: owner-wri-mathgroup at wolfram.com

Hyunho Shin wrote:
> 
> Dear Math Group Users,
> 
> In analytical integration calculus:
> 
>         f[x_] := Exp[-(x^2)/2]/Sqrt[2*Pi]
>         F[x_] := Integrate[f[z], {z, -Infinity, x}]
>         g[x_] := f[c-a*x] f[x]
>         G[x_] := F[c-a*x] f[x]
>         Integrate[ g[x], {x, d, Infinity}]
>         Integrate[ G[x], {x, d, Infinity}]
> 
> I met an error (or warning) message:
> 
>         On::none: Message SeriesData::csa not found.
> 
> What's the meaning of this message?
> 
> Thanks advance
> 
> ---------------------------------------------------------------------
> Hyunho Shin
> Assistant                       Phone +82-2-880-5434
> School of Economics             Fax   +82-2-880-6367
> Seoul National University       Email shinhh at plaza.snu.ac.kr
> Seoul, 151-742 KOREA            URL   http://plaza.snu.ac.kr/~shinhh/
> ---------------------------------------------------------------------


MMA 3.0 gave the following:

Out[5]=
       2
If[Re[a ] > -1 && d >= 0 && Re[a c] < 0, 
 
              1
  ------------------------- 
              2
  2 Sqrt[1 + a ] Sqrt[2 Pi]
 
     2          2
    c /(-2 - 2 a )         1               2
   E               (Sqrt[------] Sqrt[1 + a ] + 
                              2
                         1 + a
 
             1               2                1
      Sqrt[------] Sqrt[1 + a ] Erf[a Sqrt[--------] c] + 
                2                                 2
           1 + a                           2 + 2 a
 
                                                  2   2
                                     (-a c + d + a  d)
                                Sqrt[------------------]
                 2  2                           2
                a  c                       1 + a
      Erf[Sqrt[--------]] - Erf[------------------------]), 
                      2                 Sqrt[2]
               2 + 2 a
 
                2                   2
             -(x /2) - 1/2 (c - a x)
            E
  Integrate[-------------------------, {x, d, \[Infinity]}]]
                      2 Pi
Out[6]=
    1
---------- Integrate[If[c - a x < 0, 
Sqrt[2 Pi]
 
                              2
     1          Sqrt[(c - a x) ]
     - (1 - Erf[----------------]), 
     2              Sqrt[2]
 
                                                        2
                      1                                x /2
     Integrate[----------------, {z, -\[Infinity], c - a x}]] / E    , 
                 2
                z /2
               E     Sqrt[2 Pi]
 
   {x, d, \[Infinity]}]


Hope that helps.  If you know what the allowable values are for your
variables, these expression may be simplified.

Wilson

wfiguero at mosquito.com


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