gamma function: meaning, definition, pronunciation and examples
C2Highly technical (mathematics, physics, statistics, engineering)
Quick answer
What does “gamma function” mean?
A mathematical function that extends the factorial function to complex numbers, excluding non-positive integers.
Audio
Pronunciation
Definition
Meaning and Definition
A mathematical function that extends the factorial function to complex numbers, excluding non-positive integers.
In advanced mathematics, a complex-valued function denoted by Γ(z), central to complex analysis, probability theory (e.g., defining the Gamma distribution), and number theory. It is defined via an integral for numbers with a positive real part.
Dialectal Variation
British vs American Usage
Differences
No lexical differences. Spelling of related terms follows regional norms (e.g., 'behaviour' vs. 'behavior', 'analyse' vs. 'analyze').
Connotations
Identical technical meaning and prestige.
Frequency
Used with identical frequency in academic/technical contexts in both regions.
Grammar
How to Use “gamma function” in a Sentence
the gamma function of [argument]define the gamma function asuse the gamma function to [purpose]relate via the gamma functionVocabulary
Collocations
Examples
Examples of “gamma function” in a Sentence
verb
British English
- (No verb form)
American English
- (No verb form)
adverb
British English
- (No adverb form)
American English
- (No adverb form)
adjective
British English
- The gamma-function properties are fascinating.
- We need a gamma-function evaluation.
American English
- The gamma function properties are fascinating.
- We need a gamma function evaluation.
Usage
Meaning in Context
Business
Never used.
Academic
Core term in pure/applied mathematics, theoretical physics, advanced statistics.
Everyday
Virtually never used.
Technical
Essential in derivations involving special functions, probability distributions, asymptotic analysis.
Vocabulary
Synonyms of “gamma function”
Strong
Neutral
Weak
Vocabulary
Antonyms of “gamma function”
Watch out
Common Mistakes When Using “gamma function”
- Referring to it as a 'gamma equation' instead of a 'function'.
- Treating it as a simple generalisation without acknowledging its complex-domain intricacies.
- Incorrect pluralisation ('gamma functions' is only used when discussing different types, e.g., incomplete vs. complete).
FAQ
Frequently Asked Questions
For positive integers n, Γ(n) = (n-1)!. So it generalises the factorial, but it is defined for complex numbers (except non-positive integers).
It was first introduced by Leonhard Euler in the early 18th century, then studied further by Legendre, Gauss, and others.
In calculating probabilities for the Gamma and Chi-squared distributions, in fractional calculus, in asymptotic series, and in solutions to certain differential equations in physics.
The beta function B(x, y) can be expressed in terms of gamma functions: B(x, y) = Γ(x)Γ(y) / Γ(x+y).
A mathematical function that extends the factorial function to complex numbers, excluding non-positive integers.
Gamma function is usually highly technical (mathematics, physics, statistics, engineering) in register.
Gamma function: in British English it is pronounced /ˈɡæmə ˈfʌŋkʃ(ə)n/, and in American English it is pronounced /ˈɡæmə ˈfʌŋkʃən/. Tap the audio buttons above to hear it.
Phrases
Idioms & Phrases
- “(none specific)”
Learning
Memory Aids
Mnemonic
Γ (Gamma) extends the Factorial, like a ladder reaching from positive integers into the complex plane.
Conceptual Metaphor
A FACTORY FOR FACTORIALS; A BRIDGE FROM THE DISCRETE TO THE CONTINUOUS.
Practice
Quiz
In which field is the gamma function LEAST likely to be used?