Integrate[1/2+1/2 Erf[z],{z,-inf,0}]

• To: mathgroup at smc.vnet.net
• Subject: [mg6827] Integrate[1/2+1/2 Erf[z],{z,-inf,0}]
• From: "w.meeussen" <w.meeussen.vdmcc at vandemoortele.be>
• Date: Mon, 21 Apr 1997 02:03:28 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```hi,

Integrate[1/2+1/2 Erf[z],{z,-inf,0}]

gives :

\!\(\*
RowBox[{
\(Integrate::"idiv"\), \( : \ \),
"\<"Integral of \!\(1\/2 + \(1\/2\\ \(Erf[\(z\/\ at 2\)]\)\)\) does not \
converge on \!\({\*InterpretationBox[\(-\\[Infinity]\), \
DirectedInfinity[-1]], 0}\)."\>"}]\)

and, surprisingly,

Integrate[1/2+1/2 Erf[z],{z,-10.0,0.0}]

gives what i wanted in the first place :

1/Sqrt[2 Pi]

TWO problems:
1)      the statement that it does'nt converge MUST be wrong !

2)      if i give it floating point integration limits, then i expect a
numeric result (0.398942).

Should i consider this a (little) bug, or am i being silly?
*****************************************
a propos, the following stuff is ok:

In[16]:=
1/2+1/2 Erf[z/Sqrt[2]] /.z->-\[Infinity]
Out[16]=
0

and

In[27]:=
Integrate[1/2 Erfc[z/Sqrt[2]],{z,0,\[Infinity]}]
Out[27]=
1/Sqrt[2 Pi]

but the following needs the full power of "FullSimplify" to work out:
In[26]:=
1/2 Erfc[-z/Sqrt[2]]==1/2+1/2 Erf[z/Sqrt[2]]//FullSimplify
Out[26]=
True

Dr. Wouter L. J. MEEUSSEN
eu000949 at pophost.eunet.be
w.meeussen.vdmcc at vandemoortele.be

```

• Prev by Date: Re: Help getting values from NDSolve
• Next by Date: Re: Including Functions and Variables from another Notebook
• Previous by thread: Re: Searching for binary and ternary alloys developed with Mathematica
• Next by thread: Strange Compile Results