@article{Elliott98b,
   author =   {David Elliott},
   title =    {Sigmoidal Transformations and the Trapezoidal Rule},
   journal =  {J.~Austral.\ Math.\ Soc.~B},
   volume =   40,
   pages =    {E77--E137},
   year =     1998,
   number =   {E},
   month =    nov,
   note =     {[Online] \protect\url{http://jamsb.austms.org.au/V40/E006} [12 Nov 
               1998]},
   abstract = {A sigmoidal transformation is a one-to-one mapping of the 
               compact interval $[0,1]$ onto itself whose graph is
               $S$-shaped. After giving a formal definition, various
               mappings already given in the literature are reviewed
               in the light of the definition. At least one new
               transformation is introduced and criteria given for
               generating transformations having special properties.
               The use of these transformations in using the
               trapezoidal rule to evaluate $\int_0^1f\left( x\right)
               dx$ is then considered and asymptotic estimates of the
               truncation errors are obtained under different
               conditions. The paper concludes with some numerical
               examples.},
}