generating function — قاموس الإنجليزية

اسم

1. 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.

   كلمات ذات صلة

   moment-generating functionpower series

   مصطلحات أعمّ

   formal power series

   مصطلحات أخصّ

   exponential generating functionBell seriesDirichlet seriesLambert seriesordinary generating function

   أمثلة

   أمثلة إضافية (2)

   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.