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<div class="moz-cite-prefix">On 10/19/13 13:31, Levi M Mitze wrote:<br>
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cite="mid:C40B2F181831EF44A88CD735258278030266A720B9@MERCERMAIL.MercerU.local"
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Hi, Dr. Pounds.
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<div>I was just reading the problem you put on the fourth
homework set. Was Gauss-Laguerre quadrature covered in class
on Wednesday? (I missed class on Wednesday.) Because I don't
know what it is. I don't have it anywhere in my notes except
for a mention that it involves bounds of integration from a
constant to infinity. I can't find it in the textbook either.</div>
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<div>Levi</div>
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<br>
<font face="serif">So to use Gauss-Laguerre quadrature is defined
for functions like<br>
<br>
<img style="vertical-align: middle"
src="cid:part1.05010101.02030205@mercer.edu"
alt="$\int_0^{\infty} e^{-x} f(x) dx = \sum_{i=1}^N w_i f(x_i)$"><br>
<br>
to make it so it works for a general integration </font><font
face="serif"><font face="serif"> </font>you have to divide both
sides by <img style="vertical-align: middle"
src="cid:part2.02060305.02020900@mercer.edu" alt="$e^{-x}$">.
In other words...<br>
<br>
</font><br>
<font face="serif"><img style="vertical-align: middle"
src="cid:part3.01040100.06070103@mercer.edu"
alt="$\int_0^{\infty} f(x) dx = \sum_{i=1}^N w_i f(x_i) /
e^{-x}$"></font><font face="serif"><br>
<br>
</font><br>
<font face="serif"><font face="serif"><img style="vertical-align:
middle" src="cid:part4.00080402.03060705@mercer.edu"
alt="$\int_0^{\infty} f(x) dx = \sum_{i=1}^N w_i f(x_i)
e^{x_i}$"><br>
<br>
</font>So for the quadrature you multiply the value of your
function evaluated at the <img style="vertical-align: middle"
src="cid:part5.02000905.06090906@mercer.edu" alt="$x_i$"> point
by the exponential of <img style="vertical-align: middle"
src="cid:part5.02000905.06090906@mercer.edu" alt="$x_i$"> and
multiply this all by the weight factor <img
style="vertical-align: middle"
src="cid:part7.09070602.04090907@mercer.edu" alt="$w_i$">.<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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