Plot Gamma Function with Mathematica

Mathematica
Thread starter aredy29
Start date Feb 3, 2012
Tags

Function Gamma Gamma function Mathematica Plot

In summary, the Gamma Function is a mathematical function denoted by Γ and defined as the integral of a power function. It can be plotted using the built-in function <code>Gamma[x]</code> in Mathematica, and has several key features, including being defined for all complex numbers except non-positive integers, being a transcendental function, and satisfying a functional equation. It has various applications in research and calculations, such as in probability and statistics, and can be customized in Mathematica with options for the plot.

Feb 3, 2012

aredy29

I have a gamma function in the form of Gamma(s-1) where s can take only positive values. How can I plot this function for different value of s using Mathematica ?

Physics news on Phys.org

Feb 4, 2012

Bill Simpson

Perhaps

Plot[Gamma[s - 1], {s, 0, 10}]

1. What is the Gamma Function?

The Gamma Function is a mathematical function denoted by Γ and defined as the integral of a power function. It is used to extend the concept of factorial to real and complex numbers.

2. How do I plot the Gamma Function with Mathematica?

To plot the Gamma Function with Mathematica, you can use the built-in function Gamma[x]. This will plot the function for a given value of x. You can also use the Plot function to plot the Gamma Function over a specific range of values.

3. What are the main features of the Gamma Function?

The Gamma Function has several important features, including:

It is defined for all complex numbers except non-positive integers.
It is a transcendental function.
It has a singularity at x=0 and poles at negative integers.
It satisfies the functional equation Γ(z+1) = zΓ(z).

4. How can I use the Gamma Function in my research or calculations?

The Gamma Function has many applications in mathematics, physics, and engineering. It is commonly used in probability and statistics to calculate the factorial of non-integer numbers. It also appears in various mathematical models and equations, such as the Euler-Mascheroni constant and the Weierstrass Function.

5. Can I customize the plot of the Gamma Function with Mathematica?

Yes, you can customize the plot of the Gamma Function with various options in Mathematica, such as the range of values, the number of points, and the style of the plot. You can also add labels, legends, and other annotations to enhance the visualization of the plot.