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MathematicalFunctions

 Sequences
 The Sequences package for handling symbolic sequences

Description

 • Sequences is a package of commands for handling symbolic sequences, that is, sequences where the number of operands is unknown. Symbolic sequences enter in various formulations in mathematics. Among the most typical cases of symbolic sequences, there are:
 1. A sequence of numbers - say from n to m - frequently displayed as

$n,\mathrm{...},m$

 2. A sequence of one object, say a, repeated say p times, frequently displayed as

$\underset{}{\underset{⏟}{a,\mathrm{...},a}}$

 3. A more general sequence, as in 1., but of different objects and not necessarily numbers, frequently displayed as

${a}_{n},\mathrm{...},{a}_{m}$

 or likewise a sequence of functions $f\left(n\right),\mathrm{...},f\left(m\right)$.

In all these cases, none of n, m, or p are known: they are just symbols, or algebraic expressions, representing integer values. These most typical cases of symbolic sequences have been implemented in Maple using the $operator. Cases 1., 2. and 3. above are respectively entered as$(n .. m), a $p and a[i]$ (i = n .. m). To that implementation, the Sequences package adds two things: the typesetting of these three kinds of symbolic sequences as shown in the enumeration above, and commands to perform algebraic operations on them.

List of The Sequences Package Commands

Brief description of each command