| Author |
Comment/Response |
Bill Simpson
|
 06/20/12 11:47am
Almost always, getting back your input unchanged means that it either doesn't match any function definition OR that it cannot find a simpler form to give you a result.
Now for ideas. You have, roughly, (p+q)/r and you want the limit as n->Infinity. The numerator doesn't seem to be the real problem, other than not knowing whether b0>b1 or b0<b1, m0>x or m0<x, etc, etc, etc. If you could provide it assumptions to answer those questions then I think it could find the limit of the numerator.
In[8]:= Simplify[Assuming[{b0>b1>0,m0>m1,x∈Reals&&n∈Integers}, Limit[(2 π)^(-(1/2)) (((b0-b1) (b0+b1) (m0-m1) (-b1^2 (m0+m1 (-1+ n)+3 m0 n-4 n x)+b0^2 (m0-m1+m0 n+3 m1 n-4 n x)) +2 n (b1^2 (m0-x)+b0^2 (-m1+x))^2 (HarmonicNumber[(b0^2 n)/(b0^2-b1^2)]-HarmonicNumber[(b1^2 n)/(b0^2- b1^2)])) /(4 (b0-b1)^3 (b0+b1)^3)),n\[Rule]Infinity]]]
Out[8]= DirectedInfinity[Sign[b0]^8* Sign[b1]^8*Sign[(b0^2 - b1^2)*(m0 - m1)* (-(b1^2*(3*m0 + m1 - 4*x)) + b0^2*(m0 + 3*m1 - 4*x)) + 2*(b1^2*(m0 - x) + b0^2*(-m1 + x))^2* Log[b0^2/(b0^2 - b1^2)] - 2*(b1^2*(m0 - x) + b0^2*(-m1 + x))^2* Log[b1^2/(b0^2 - b1^2)]]]
That looks like Limit isn't picking up some of the assumptions. If that could be resolved then this should be a fairly simple limit for your numerator.
The denominator has the same problem with b0 and b1, but I don't know whether even with that resolved whether it will be able to find the limit for that.
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