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<font face="serif">First -- please forgive me for not getting back
to you all sooner about this. I got home from campus on
Wednesday with a fever that blossomed into something that kept me
bedridden for two days.<br>
<br>
Anyway, in looking at problems in the text that deal with the
derivatives of Hermite polynomials, you have to remember that the
polynomial can be constructed as shown in the equation just above
Table 3.16. In that equation the divided differences are the Q
values that you calculate in Algorithm 3.3.<br>
<br>
As way of an example, looking at problem 1a on page 139, I get the
following Q values<br>
<br>
Q00 = 17.56492<br>
Q11 = 3.116256<br>
Q22 = 0.05948<br>
Q33 = -0.002022222<br>
<br>
Which translates into<br>
<br>
<img style="vertical-align: middle"
src="cid:part1.09020800.02060601@mercer.edu" alt="$H(x) =
Q_{00} + Q_{11} (x-8.3) + Q_{22} (x-8.3)^2 + Q_{33} (x-8.3)^2
(x-8.6)$"><br>
<br>
this can be simplified (approximately) to...<br>
<br>
<img style="vertical-align: middle"
src="cid:part2.09090608.07070001@mercer.edu" alt="$H(x) =
-0.00202222 x^3 + 0.11044 x^2 + 1.70088 x - 3.00435$"><br>
<br>
which can easily have it's derivative taken wrt <img
style="vertical-align: middle"
src="cid:part3.02060800.08080805@mercer.edu" alt="$x$">. <br>
<br>
My recommendation is to use your program to generate the Q values
for the Hermite polynomial, then enter the polynomial into Sage or
Mathematica in its "pre-simplified" canonical form -- and let the
CAS simplify the expression and provide you with the derivative.
<br>
<br>
<br>
<br>
</font>
<pre class="moz-signature" cols="72">--
Andrew J. Pounds, Ph.D. (<a class="moz-txt-link-abbreviated" href="mailto:pounds_aj@mercer.edu">pounds_aj@mercer.edu</a>)
Professor of Chemistry and Computer Science
Mercer University, Macon, GA 31207 (478) 301-5627
<a class="moz-txt-link-freetext" href="http://faculty.mercer.edu/pounds_aj">http://faculty.mercer.edu/pounds_aj</a>
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