re: Same Limit in v5.2 and v6.0 - conclusion, I hope...
- To: mathgroup at smc.vnet.net
- Subject: [mg78004] re: Same Limit in v5.2 and v6.0 - conclusion, I hope...
- From: jrc <jrchaff at mcn.net>
- Date: Thu, 21 Jun 2007 05:42:54 -0400 (EDT)
This may be of use to others, so I furnish the conclusion, prompted by yet another offline communication. Here is the code that works in v6.0: (I have been advised to post 'actual mathematica code' - so some lines may have to be text...) In[1]= $Assumptions = a > 0 && k1 > 0 && k2 > 0 && Element[x, Reals] Out[1]= a > 0 && k1 > 0 && k2 > 0 && x e(in) Reals In[2]= i1b = (1/a)*Integrate[Exp[-i*k2*x]*Exp[i*k1*x],x] 2*Sin[(1/2)*a*(k1-k2)] Out[2]= ------------------------ a*(k1-k2) In[3]= Limit[i1b, a -> Infinity] Out[3]= 0 ---------------- This is the obviously correct result, since it is the same limit as sin(x)/x at infinity. However, the use of $Assumptions is in fact different in v6.0, and I can find no instance in the 'new' 6.0 documentation that shows this, including the little 'new in 6' links. In v5.2, the assumptions statement, shown in a number of books, $Assumptions = {a > 0, k1 > 0, k2 > 0, x e(in) Reals} works perfectly fine. In fact, the use of a list enclosed in brackets is shown in one of the examples in the 5.2 Help Browser rather clearly under '$Assumptions'. But this form will not work in 6.0 until three modifications are made: 1) The list should be joined with Boolean 'and': "&&" operators; 2) Apparently one must use the 'Element' function instead of the funny 'e' symbol (not sure this is necessary); But finally, strangely enough and this *IS* a change from 5.2, enclosing the list in brackets does not work in 6.0 - at least for the 'Limit' function. Once again, I would like to see a clear statement of differences in 6.0 for the oft-used functions. "$Assumptions" falls into this category. jrc