The art of manipulating an algebraic expression into the desired form.

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Differing behaviour of GeneratingFunction with different numbers of parameters

When given a single variable sequence, GeneratingFunction is automatically expressed in the most "direct form", for example, ...
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Apart may use Padé method: what's that?

How does Apart work? The page tutorial/SomeNotesOnInternalImplementation#7441 says, "Apart ...
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115 views

Solving recursion relations using Mathematica

I want to solve the recursion relation given in equation 2.7(a/b) on page $6$ of this paper. (..the initial seed is $F_1 = G_1 = 1$ and the functions $\alpha$ and $\beta$ are defined on page $5$ in ...
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Cyclic Noncommutative Multiplication

I work with traces of long matrix products and I want mathematica to employ the cyclicity when simplifying. I use this redefinition of the non-commutative multiplication: ...
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Need conditions for DSolve

If I have differential equation of fourth order with four solutions $\alpha _1,\alpha _2,-\alpha _1,-\alpha _2 $ where we have appearing the solutions in the form $e^{\text{$i\alpha $}_1 ...