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m v2.05b - Bot T20 CW#61 - Fix errors for CW project (Reference before punctuation) |
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When the product <math>{C}_{n} {D}_{n}</math> approaches unity with increasing <math>n</math>, it is hoped that <math>{f}_{n}</math> has converged to <math>f</math>.<ref name="numerical-recipes">{{Cite book |last1=Press |first1=W.H. |title=Numerical Recipes: The Art of Scientific Computing |last2=Teukolsky |first2=S.A. |last3=Vetterling |first3=W.T. |last4=Flannery |first4=B. P. |publisher=Cambridge University Press |year=2007 |edition=3rd |pages=207–208}}</ref>
Lentz's algorithm has the advantage of side-stepping an inconvenience of the Wallis-Euler relations, namely that the numerators <math>A_n</math> and denominators <math>B_n</math> are prone to grow or diminish very rapidly with increasing <math>n</math>. In direct numerical application of the Wallis-Euler relations, this means that <math>A_{n-1}</math>, <math>A_{n-2}</math>, <math>B_{n-1}</math>, <math>B_{n-2}</math> must be periodically checked and rescaled to avoid floating-point overflow or underflow.<ref name="numerical-recipes" />
== Applications ==
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