<title>Continued Fraction Evaluation</title>
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<div class="titlepage"><div><div><h3 class="title">
the continued fraction described by the <span class="emphasis"><em>generator</em></span> type
argument. The functions with an "_a" suffix evaluate the fraction:
</p>
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- <span class="inlinemediaobject"><img src="../../../equations/fraction2.svg"></span>
- </p>
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+ <span class="inlinemediaobject"><img src="../../../equations/fraction2.svg"></span>
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+ </p></blockquote></div>
<p>
and those with a "_b" suffix evaluate the fraction:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../equations/fraction1.svg"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../equations/fraction1.svg"></span>
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<p>
This latter form is somewhat more natural in that it corresponds with the
usual definition of a continued fraction, but note that the first <span class="emphasis"><em>a</em></span>
= 1.618033989...</a> can be computed from the simplest continued fraction
of all:
</p>
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- <span class="inlinemediaobject"><img src="../../../equations/fraction3.svg"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../equations/fraction3.svg"></span>
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<p>
We begin by defining a generator function:
</p>
and the <span class="emphasis"><em>b</em></span>'s when evaluating special functions by continued
fractions, for example the tan function is defined by:
</p>
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- <span class="inlinemediaobject"><img src="../../../equations/fraction4.svg"></span>
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+ <span class="inlinemediaobject"><img src="../../../equations/fraction4.svg"></span>
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<p>
So its generator object would look like:
</p>
Now we'll look at a couple of complex number examples, starting with the
exponential integral which can be calculated via:
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+ <span class="inlinemediaobject"><img src="../../../equations/expint_n_3.svg"></span>
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<p>
So our functor looks like this:
</p>
there is only one special function in our code which uses that variant, and
it's the upper incomplete gamma function (Q), which can be calculated via:
</p>
-<p>
- <span class="inlinemediaobject"><img src="../../../equations/igamma9.svg"></span>
- </p>
+<div class="blockquote"><blockquote class="blockquote"><p>
+ <span class="inlinemediaobject"><img src="../../../equations/igamma9.svg"></span>
+
+ </p></blockquote></div>
<p>
In this case the first couple of terms are different from the rest, so our
fraction will start with the first "regular" a term:
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