GAMMA FUNCTION Meaning and
Definition
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The gamma function is a mathematical function defined for complex numbers, that extends the concept of a factorial to non-integer values. It is denoted by the Greek letter γ (gamma) and is defined as the integral of the function x^(s-1) * e^(-x) from 0 to infinity, where s is the argument of the gamma function.
The gamma function plays a pivotal role in mathematical analysis and has applications in various fields, such as statistics, physics, and engineering. It provides a way to generalize the factorial function, allowing for the computation of factorials for non-integer values. In fact, the gamma function is equal to (s-1)! for positive integer values of s.
One important property of the gamma function is its analytic continuation, which implies that it can be defined for complex numbers with negative real parts. This property makes it a valuable tool in complex analysis and allows for the evaluation of integrals involving complex variables.
Furthermore, the gamma function satisfies a recurrence relation known as the reflection formula, which states that gamma(s) * gamma(1-s) = π / sin(πs), for any complex number s.
Overall, the gamma function is a fundamental mathematical tool that extends the concept of factorials to non-integer values and has wide-ranging applications in many areas of mathematics and science.
Common Misspellings for GAMMA FUNCTION
- famma function
- vamma function
- bamma function
- hamma function
- yamma function
- tamma function
- gzmma function
- gsmma function
- gwmma function
- gqmma function
- ganma function
- gakma function
- gajma function
- gamna function
- gamka function
- gamja function
- gammz function
- gamms function
- gammw function
- gammq function
Etymology of GAMMA FUNCTION
The word "gamma" in "gamma function" is derived from the Greek letter "gamma" (Γ), which is the uppercase form of the third letter in the Greek alphabet. The gamma function was introduced and named by the Swiss mathematician Leonhard Euler in the 18th century. Euler chose the letter "gamma" to represent this function as it had not been used for any other mathematical purpose at the time. The use of the term "gamma function" has since been retained to refer to the specific mathematical function introduced by Euler.
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