Integration of Gaussians

• To: mathgroup at yoda.physics.unc.edu
• Subject: Integration of Gaussians
• From: lsf at holmes.astro.nwu.edu (Sam Finn)
• Date: Mon, 9 Mar 92 21:08:00 CST

```Still a few bugs in the system . . . This is with the patch posted by
withoff at wri.com on 25 January 1992. It also happens on a next running
Mathematica version 2.0 (November 14 1991).

Mathematica 2.0 for SPARC
-- Terminal graphics initialized --

In[1]:= f[x_,a_,sigma_] := Exp[-(x-a)^2/sigma^2]

In[2]:= Integrate[f[x,a,sigma],{x,-Infinity,Infinity}]

2      2
a /sigma                2         a
Out[2]= (E          Sqrt[Pi] sigma  Erf[----------] +
Abs[sigma]

2          2      2
3    a          a /sigma
>      a Abs[sigma] HypergeometricU[1, -, ------]) / (E          Abs[sigma])
2       2
sigma

In[3]:= Table[% /. sigma->1,{a,-1,1,0.5}]

Infinity::indet: Indeterminate expression 0. 1 ComplexInfinity encountered.

3
-(E Sqrt[Pi] Erf[1]) - HypergeometricU[1, -, 1]
2
Out[3]= {-----------------------------------------------,
E

>    0.778801 (-1.09128 - 0.668335 Sqrt[Pi]), Indeterminate,

>    0.778801 (1.09128 + 0.668335 Sqrt[Pi]),

>    0.367879 (0.757872 + 2.2907 Sqrt[Pi])}

In[4]:= N[%]

Out[4]= {-1.77245, -1.77245, Indeterminate, 1.77245, 1.77245}

In[5]:= ^D

```

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