Nomina
A formal power series with one indeterminate, whose coefficients encode a sequence that can be studied by algebraic manipulation of the series; any one of several generalizations, such as to encode more than one sequence or use more than one indeterminate.
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- Istilah yang lebih umum
- Istilah yang lebih khusus
- exponential generating functionBell seriesDirichlet seriesLambert seriesordinary generating function
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A generating function is a device somewhat similar to a bag. Instead of carrying many little objects detachedly, which could be embarrassing, we put them all in a bag, and then we have only one object to carry, the bag.
Most often generating functions arise from recurrence formulas. Sometimes, however, from a generating function you will find a new recurrence formula, not the one you started with, that gives new insights into the nature of your sequence.
2003, Sergei K. Lando (author & translator), Lectures on Generating Functions, American Mathematical Society.