Everything about Gamma function
Extension of the factorial function
In mathematics, the gamma function, denoted by , is the most common extension of the factorial function to complex numbers. First studied by Daniel Bernoulli, the gamma function is defined for all complex numbers except non-positive integers, and satisfies for every positive integer . The gamma function can be defined via a convergent improper integral for complex numbers with positive real part: The gamma function then is defined in the complex plane as the analytic continuation of this integral function: it is a meromorphic function which is holomorphic except at zero and the negative integers, where it has simple poles. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Gamma functionA 5-minute orientation
- Skim a recent paper: On the Barnes double gamma functionInfluential work since 2022
- Pick up a classic book: Tables of the incomplete Þ-functionThe most-reprinted book on the subject
- Read the landmark paper: Note on the Gamma FunctionCited 141 times
- Go sideways: Reciprocal gamma functionA closely related topic
- Go sideways: Particular values of the gamma functionA closely related topic
📖 Definitions
Noun A meromorphic function which generalizes the notion of factorial to complex numbers and has singularities at the nonpositive integers; any of certain generalizations or analogues of said function, such as extend the factorial to domains other than the complex numbers.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Note on the Gamma Function
Inequalities for the gamma function
On gamma function inequalities
Simple Generation of Gamma, Gamma–Gamma, and K Distributions With Exponential Autocorrelation Function
Some gamma function inequalities
Inequalities for Gamma Function Ratios
A completely monotone function related to the Gamma function
Inequalities for the gamma function
🆕 Influential since 2022
On the Barnes double gamma function
ON THE CUMULATIVE DISTRIBUTION FUNCTION OF THE VARIANCE-GAMMA DISTRIBUTION
Euler Phi Function and Gamma Function Based Elliptic Curve Encryption for Secured Group Communication
On Some Bounds for the Gamma Function
On Some Asymptotic Expansions for the Gamma Function
📚 Books worth reading
Tables of the incomplete Þ-functionKarl Pearson · 1922
GammaJulian Havil · 2003
Einführung in die Theorie der GammafunktionEmil Artin · 1931
Solved problems in analysisOrin J. Farrell, Bertram Ross · 1971
Exercices de calcul intégral sur divers ordres de transcendantes et sur les quadraturesAdrien-Marie Legendre · 1811
G. Lejeune-Dirichlets Vorlesungen über die Lehre von den einfachen und mehrfachen bestimmten IntegralenPeter Gustav Lejeune-Dirichlet · 1904
Théorie de la fonction gammaHenri Jules Joseph Limbourg · 1859
Traité des fonctions elliptiques et des intégrales eulériennesAdrien-Marie Legendre · 1825
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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