zoom within the last plot computed using 'Evalf' related to concatenated Taylor expansions used when performing numerical computations of Heun or Appell functions
(optional) list with two numbers, where 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. The default value is [1, 1].
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):
Consider one of the special values of AppellF1, a case where the function can be represented by a 2F1 hypergeometric function
F1 ≔ %AppellF14.0, 2.0, .3, 2.3, 1.12, 1.1
The left-hand side is AppellF1 in inert form, to avoid the automatic representation in terms of 2F1 functions, while the right-hand side involves only a hypergeometric 2F1 function. Evaluate this expression numerically
Compute the same but now using a concatenated Taylor series expansion, and displaying a plot showing the centers and path of the Taylor expansions used and no other information
CPU time elapsed during evaluation: .78e-1 seconds
Zoom closer to the evaluation point 1.1, extending 1/50 to the left and right of 1.1
In this Taylor approach, each expansion around a point is used to reach up to 95/100 of the radius of convergence before starting another expansion. Reduce that to 1/2, compute internally at Digits = 50 (but return as if computing with Digits = 10)
CPU time elapsed during evaluation: .281 seconds
Use Zoom to zoom closer to the point z=1.1
The MathematicalFunctions[Evalf][Zoom] command was introduced in Maple 2017.
For more information on Maple 2017 changes, see Updates in Maple 2017.
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