Assertion: generating function | /r/HasProperty | equivalent
Facets:
value: to the factorial moment generating function
type: OTHER
Source sentences:
text: In other words, the properties that a sequence be P-recursive and have a holonomic generating function are equivalent.
text: } It follows from Property 1 that if random variables X and Y have probability-generating functions that are equal, G X = G Y {\displaystyle G_{X}=G_{Y}} p X = p Y {\displaystyle p_{X}=p_{Y}} X and Y have identical probability-generating functions, then they have identical distributions.
text: The probability generating function is also equivalent to the factorial moment generating function, which as E ⁡ [ z X ] {\displaystyle \operatorname {E} \left[z^{X}\right]} can also be considered for continuous and other random variables.