a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are...

In probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability...

probability generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the...

are defined using the cumulant-generating function K(t), which is the natural logarithm of the moment-generating function: K ( t ) = log ⁡ E ⁡ [ e t X ]...

specifically in Hamiltonian mechanics, a generating function is, loosely, a function whose partial derivatives generate the differential equations that determine...

of a sequence's generating function provides a method of converting the generating function for one sequence into a generating function enumerating another...

canonical. The various generating functions and its properties tabulated below is discussed in detail: The type 1 generating function G1 depends only on the...

an exponential function of the square root of its argument. The multiplicative inverse of its generating function is the Euler function; by Euler's pentagonal...

moment-generating function, and call the logarithm of the characteristic function the second cumulant generating function. Characteristic functions can be...

would be ⁠ 1 15 . {\displaystyle {\tfrac {1}{15}}.} ⁠ The moment-generating function of the continuous uniform distribution is: M X = E ( e t X ) = ∫...