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