The Zoom command is used to zoom within the last plot computed using Evalf using a concatenated Taylor expansions approach when performing numerical evaluations of Heun or Appell functions. This command is useful to understand how the method of a sequence of concatenated Taylor expansions work.

When called with the extra argument [n, m], $n$ represents the origin of the returned plot and $m$ indicates the width to the left and to the right of $n$ where the plot is being zoomed. Calling Zoom with no arguments is the same as calling it with the optional argument [1, 1].

Initialization: Load the command and package and set the display of special functions in output to typeset mathematical notation (textbook notation):

$\mathrm{with}\left(\mathrm{MathematicalFunctions}\,\mathrm{Evalf}\right)$

$\left[\mathrm{Evalf}\right]$

$\mathrm{with}\left(\mathrm{MathematicalFunctions}:-\mathrm{Evalf}\right)\;\mathrm{Typesetting}:-\mathrm{EnableTypesetRule}\left(\mathrm{Typesetting}:-\mathrm{SpecialFunctionRules}\right)\:$

$\left\{\mathrm{Add}\,\mathrm{Evalb}\,\mathrm{Zoom}\,\mathrm{QuadrantNumbers}\,\mathrm{Singularities}\,\mathrm{GenerateRecurrence}\,\mathrm{PairwiseSummation}\right\}$

$\mathrm{F1} ≔ \mathrm{\%AppellF1}\left(4.0\, 2.0\, .3\, 2.3\, 1.12\, 1.1\right)$

$\mathrm{F1}≔F_1\left(4.0\,2.0\,0.3\,2.3\,1.12\,1.1\right)$

$\mathrm{F1}=\mathrm{value}\left(\mathrm{convert}\left(\mathrm{F1}\,\mathrm{rational}\right)\right)$

$F_1\left(4.0\,2.0\,0.3\,2.3\,1.12\,1.1\right)=10000{}_{2}F_1\left(2,4;\frac{23}{10};-\frac{1}{5}\right)$

$\mathrm{evalf}\left(\right)$

$5325.710910=5325.710910$

$\mathrm{Evalf}\left(\,\mathrm{usetaylor}\,\mathrm{time}\,\mathrm{plot}\,\mathrm{quiet}\right)$

$\mathrm{CPU\; time\; elapsed\; during\; evaluation:\; .78e-1\; seconds}$

$5325.710910+1.{10}^{\mathrm{-13}}\mathrm{I}=5325.710910$

$\mathrm{Zoom}\left(\left[1.1\,\frac{1}{50}\right]\right)$

$\mathrm{Evalf}\left(\,50\,\mathrm{usetaylor}\,R=\frac{1}{2}\,\mathrm{time}\,\mathrm{plot}\,\mathrm{zoom}=\left[1\,\frac{1}{2}\right]\,\mathrm{quiet}\right)$

$\mathrm{CPU\; time\; elapsed\; during\; evaluation:\; .281\; seconds}$

$5325.710910+1.410240821{10}^{\mathrm{-52}}\mathrm{I}=5325.710910$

$\mathrm{Zoom}\left(\left[1.1\,\frac{1}{15}\right]\right)$

The MathematicalFunctions[Evalf][Zoom] command was introduced in Maple 2017.

For more information on Maple 2017 changes, see Updates in Maple 2017.