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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
Copyright 1988-91 Wolfram Research, Inc.
-- 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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