Formal Power Series
The convert/FormalPowerSeries functionality was completely rewritten for Maple 2022. It offers a number of advantages over previous versions:
Closed-form solutions can be found in a number of cases where previous versions failed.
Solutions in terms of -fold hypergeometric sequences for arbitrary positive integers are now supported in more cases than before.
Notwithstanding the name, formal Laurent and Puiseux series (i.e., with negative or fractional exponents) can be computed as well, now in more cases than before.
convert/FormalPowerSeries will automatically attempt to return the series coefficients in purely real form, making the previous option makereal obsolete.
In a number of cases, the new code returns more compact answers than previous versions.
If a closed form expression for the power series coefficients cannot be found, and a recurrence relation of degree 1 or 2 exists, it will be returned instead. Previously, only linear recurrences could be computed, and would only be returned if option recurrence was specified.
When a recurrence relation is returned, now the initial conditions are given as well.
Additional options give more control over the underlying algorithm(s) used and the form of the output.
Maple 2021
Maple 2022
More closed-form solutions, notably, for sums of several terms and Puiseux solutions.
Solutions in purely real form by default.
More compact answers.
Recurrence relations returned automatically if no closed form can be found, with initial conditions. Non-linear (degree 2) recurrences can be computed.
New method option (by default, all three methods are tried in sequence).
New output option (default: combined).
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