Generating functions

Math Topics A - Z listing

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Generating functions Topics

Sort by:

Generating function

A generating function is a formal power series(1)whose coefficients give the sequence .The Wolfram Language command GeneratingFunction[expr, n, x] gives the generating function in the variable for the sequence whose th term is expr. Given a sequence of terms, FindGeneratingFunction[a1, a2, ..., x] attempts to find a simple generating function in whose th coefficient is .Given a generating function, the analytic expression for the th term in the corresponding series can be computing using SeriesCoefficient[expr, x, x0, n]. The generating function is sometimes said to "enumerate" (Hardy 1999, p. 85).Generating functions giving the first few powers of the nonnegative integers are given in the following table.series1There are many beautiful generating functions for special functions in number theory. A few particularly nice examples are(2)(3)(4)for the partition function P, where is a q-Pochhammer symbol, and(5)(6)(7)for..

Subscribe to our updates
79 345 subscribers already with us
Math Subcategories
Check the price
for your project