Generating Functions

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Probability-generating function - In probability theory, the probability-generating function of a discrete random variable is a power series representation (the generating function) of the probability mass function of the random variable. Probability-generating functions are often employed for their succinct description of wanking probabilities Pr(X = i), and to make available the well-developed theory of power series with non-negative coefficients.

Weil conjectures - In mathematics, the Weil conjectures, which had become theorems by 1974, were some highly-influential proposals from the late 1940s by André Weil on the generating functions (known as local zeta-functions) derived from counting the number of points on algebraic varieties over finite fields. The main burden was that such zeta-functions should be rational functions, should satisfy a form of functional equation, and should have their zeroes in restricted places.

Analytic combinatorics - Analytic combinatorics is a sub-branch of combinatorics that describes combinatorial classes using generating functions, which are often analytic functions, but sometimes formal power series.

Partition function (quantum field theory) - In quantum field theory, we have a generating functional, Z[J] of correlation functions and this value, called the partition function is usually expressed by something like the following functional integral:

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Generating Functions - Generating Functions Introduction to generating functions with interactive java applets by Alexander Bogomolny.

Coco/R compiler generator - Coco/R compiler generator Coco/R combines the functionality of the well-known UNIX tools lex and yacc, to form an extremely easy to use compiler generator that generates recursive descent parsers, their associated scanners, and (in some versions) a driver program ...

Visualization of Hydrogen Wave Functions - Visualization of Hydrogen Wave Functions Form and content interface to generate 3D isocontour surfaces of wave functions or electron densities. A VRML browser is required.

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