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How can I solve this one?

Posted 9 years ago

How can I solve this one in mathematic? Dose a limit [Tau to t] would work?

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Thanks!

POSTED BY: Jie Li

Hi, it helps when you put your equation in Mathematica format I assume that symbol in the exponent is a Pi and not an n and that L is greater than zero:

In[72]:= Clear["Global`*"]

In[73]:= sol = 
 Integrate[Exp[-L/(Pi (t - \[Tau]))]/Sqrt[t - \[Tau]], \[Tau]]

Out[73]= -2 E^(-(L/(\[Pi] (t - \[Tau])))) Sqrt[t - \[Tau]] - 
 2 Sqrt[L] Erf[Sqrt[L]/(Sqrt[\[Pi]] Sqrt[t - \[Tau]])]

In[74]:= l1 = 
 Limit[sol, \[Tau] -> t, Assumptions -> L > 0, Direction -> 1]

Out[74]= -2 Sqrt[L]

In[75]:= l2 = 
 Limit[sol, \[Tau] -> 0, Assumptions -> L > 0, Direction -> -1]

Out[75]= -2 E^(-(L/(\[Pi] t))) Sqrt[t] - 
 2 Sqrt[L] Erf[Sqrt[L]/(Sqrt[\[Pi]] Sqrt[t])]

In[76]:= l1 - l2

Out[76]= -2 Sqrt[L] + 2 E^(-(L/(\[Pi] t))) Sqrt[t] + 
 2 Sqrt[L] Erf[Sqrt[L]/(Sqrt[\[Pi]] Sqrt[t])]
POSTED BY: Kay Herbert
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