Incomplete Gamma Function Explorer

Explore the Incomplete Gamma Functions, which are generalizations of the factorial function used in statistics and physics.

Parameters

Shape Parameter (s)

Upper Limit (x)

Calculation Mode

Function Result

0.26424

Lower γ(s, x)

What is the Incomplete Gamma Function?

The Gamma function Γ(s) is an extension of the factorial function to complex numbers. The incomplete versions break this integral into two parts.

💡

Pro Tips

Note: γ(s, x) + Γ(s, x) = Γ(s) (The complete function).

Fun Facts

"In statistics, the cumulative distribution function of the Gamma and Chi-squared distributions is expressed using the incomplete gamma function."
"If s is a positive integer, γ(s, x) = (s-1)! [1 - e^{-x} Σ (x^k / k!)]."
"It appears frequently in regularizing integrals in quantum field theory."

Formula: γ(s, x) = ∫₀ˣ t^{s-1} e^{-t} dt

Used with this

Similar tools that might be useful

Complex Number Form Converter

Convert between rectangular (a + bi) and polar (r∠θ) forms of complex numbers.

AAA Triangle Calculator

Analyze triangle proportionality and similarity when all three angles are known.

AAS Triangle Calculator

Solve a triangle when two angles and one non-included side are known.