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Generating Functions from Interactive Mathematics Miscellany and Puzzles (757 words) |
 | A generating function is a clothesline on which we hang up a sequence of numbers for display. |
| In this sense, the term generating function is not quite consistent in that the operation of substituting a number for x in order to establish the value of the series at that point, is not legal. |
| is the generating function of the sequence of the binomial coefficients |
| JSSM- 2006, Vol.5, Issue 4, 567 - 574 (2943 words) |
| The mathematical method of generating functions is used to show that the likelihood of long matches can be substantially reduced by using the tiebreak game in the fifth set, or more effectively by using a new type of game, the 50-40 game, throughout the match. |
| The cumulant generating function (taking the natural logarithm of the moment generating function), can also be used to calculate the parameters of the distribution in a tennis match. |
| The cumulant generating function is particularly useful for calculating the parameters of distributions for the number of points in a tiebreaker match, since the critical property of cumulant generating functions is that they are additive for linear combinations of independent random variables. |
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