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.

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Pro Tips

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

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