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Everything about Generating function
Formal power series
In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series. Generating functions are often expressed in closed form, by some expression involving operations on the formal series. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Generating functionA 5-minute orientation
- Skim a recent paper: A mechanism of gene evolution generating mucin functionInfluential work since 2022
- Pick up a classic book: Real AnalysisThe most-reprinted book on the subject
- Read the landmark paper: Generating function for generalized function of two variablesCited 44 times
- Go sideways: Stirling polynomialsA closely related topic
- Go sideways: Cyclotomic polynomialA closely related topic
📖 Definitions
Noun A formal power series with one indeterminate, whose coefficients encode a sequence that can be studied by algebraic manipulation of the series; any one of several generalizations, such as to encode more than one sequence or use more than one indeterminate.
🏆 Landmark papers (most cited)
Generating function for generalized function of two variables
The Generating Function of Jacobi Polynomials
The relative information generating function
Empirical probability generating function
The Cumulant Generating Function Estimation Method
Generating function for angular momentum multiplicities
Generating a function for network delay
Generating function for web diagrams
🆕 Influential since 2022
A mechanism of gene evolution generating mucin function
Information Generating Function of Record Values
Generating Function for Projected Entangled-Pair States
Cumulative information generating function and generalized Gini functions
Estimating Project Cost under Uncertainty Using Universal Generating Function Method
📚 Books worth reading
Real AnalysisH. L. Royden, Patrick Fitzpatrick · 1963
Computability and logicGeorge Boolos, Richard C. Jeffrey · 1974
Negotiating the complexities of qualitative research in higher educationSusan R. Jones · 2006
Time Series AnalysisGeorge E. P. Box, Gwilym M. Jenkins · 1970
Functions of Several VariablesWendell Fleming, W. H. Fleming · 1963
PrecalculusEarl William Swokowski, Jeffery Cole · 1986
Elementary mathematical modelingMary Ellen Davis, C. Edwards · 2000
Asymptotic behavior and stability problems in ordinary differential equationsLamberto Cesari · 1959
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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