Moment Generating Functions
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چکیده
1 Generating Functions 1.1 The ordinary generating function We define the ordinary generating function of a sequence. This is by far the most common type of generating function and the adjective “ordinary” is usually not used. But we will need a different type of generating function below (the exponential generating function) so we have added the adjective “ordinary” for this first type of generating functio. Definition 1. Suppose that a0, a1, . . . is a sequence (either infinite or finite) of real numbers. Then the ordinary generating function F (t) of the sequence is the power series F (t) = a0 + a1t+ a2t 2 + · · · = ∞
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