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MathGroup Archive 2006

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Re: Integration Bug

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65259] Re: Integration Bug
  • From: "Valeri Astanoff" <astanoff at yahoo.fr>
  • Date: Wed, 22 Mar 2006 06:13:51 -0500 (EST)
  • References: <dvj4s8$1j$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Chris,

Seems to me that if you convert to Ei form,
care has to be taken of the argument sign :

In[1]:=toEiForm = {CosIntegral[x_ /; x \[Element] Reals] ->
     (1/2)*ExpIntegralEi[(-I)*x] + (1/2)*ExpIntegralEi[I*x] +
      I*Pi*(1 - UnitStep[x]), SinIntegral[x_ /; x \[Element] Reals] ->
     (1/2)*I*(ExpIntegralEi[(-I)*x] - ExpIntegralEi[I*x] +
I*Pi*Sign[x])};

In[2]:={CosIntegral[1],CosIntegral[1] /. toEiForm}
Out[2]={CosIntegral[1], ExpIntegralEi[-I]/2 + ExpIntegralEi[I]/2}

In[3]:=%//N
Out[3]={0.337404, 0.337404 + 0.*I}

In[4]:={CosIntegral[-1],CosIntegral[-1] /. toEiForm}
Out[4]={CosIntegral[-1], I*Pi + ExpIntegralEi[-I]/2 +
ExpIntegralEi[I]/2}

In[5]:=%//N
Out[5]={0.337404 + 3.14159*I, 0.337404 + 3.14159*I}


hth

Valeri Astanoff


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