I What is the Gamma Function and Its Significance in Mathematics?

I
Thread starter iDimension
Start date Jun 14, 2017

AI Thread Summary

The Gamma function is defined as Γ(n) = ∫_0^∞ t^(n-1)e^(-t) dt, serving as a generalization of the factorial function for non-integer values of n. It extends the concept of factorials beyond whole numbers, allowing for calculations involving complex and fractional values. The discussion highlights a common misunderstanding regarding the integration variable, emphasizing that it should be over t, not n. The significance of the Gamma function lies in its applications across various fields of mathematics, including probability and statistics. Understanding the Gamma function is crucial for advanced mathematical concepts and analyses.

Jun 14, 2017

iDimension

\Gamma(n)=\int_0^\infty\,t^{n-1}e^{-t}dn

What is it and what does it mean? Thanks.

Mathematics news on Phys.org

Jun 14, 2017

gleem

Science Advisor

Education Advisor

I believe that you are trying to write the definition of the Gamma functions but. the integrations should be over the parameter t not n. The Gamma functions is the generalization of the factorial form n! for non integral values of n.

Jun 14, 2017

BvU

Science Advisor

Homework Helper

https://en.wikipedia.org/wiki/Gamma_function

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...

View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

View full post »

Thread 'Fixing Things Which Can Go Wrong With Complex Numbers'

Greg tells me the feature to generate a new insight announcement is broken, so I am doing this: https://www.physicsforums.com/insights/fixing-things-which-can-go-wrong-with-complex-numbers/

View full post »