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Maths Gamma Function
Calculate the Gamma function Γ(z), the log Gamma function ln(Γ(z)), the incomplete lower Gamma function γ(z,x), the incomplete upper Gamma function Γ(z,x), the incomplete lower Gamma unit function PL(z,x), the incomplete upper Gamma unit function PU(z,x). The Gamma function is a continuous form of the integer factorial: `n! = Γ(n + 1) ` The Gamma function is recursive for values greater than 1 or less than 0 (z > 1 or z < 0). `Γ(z + 1) = z Γ(z) ` The Gamma function is invalid if z equals zero, or if z is a negative integer. The lower incomplete Gamma unit functions are defined as `PL(z,x) = γ(z,x) / Γ(z) `
`PU(z,x) = Γ(z,x) / Γ(z) ` Use the Result Plot option to plot the Gamma functions versus z. Reference : Numerical Recipes, The Art Of Scientific Computing, Press, Teukolsky, Vetterling, Flannery, Cambridge University Press Change Module :
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CALCULATOR : Gamma Function (Lanczos Approximation) [FREE] ±
Calculate the Gamma function Γ(z), the log Gamma function ln(Γ(z)), the incomplete lower Gamma function γ(z,x), the incomplete upper Gamma function Γ(z,x), the incomplete lower Gamma unit function PL(z,x), the incomplete upper Gamma unit function PU(z,x). The Gamma function is invalid if z equals zero, or if z is a negative integer. Use the Result Plot option to plot the Gamma functions versus z. Tool InputTool Output- Γ(z) : Gamma Function
- Γ(z,x) : Upper Incomplete Gamma Function
- γ(z,x) : Lower Incomplete Gamma Function
- PL(z,x) : Lower Incomplete Unit Gamma Function (γ(z,x) / Γ(z))
- PU(z,x) : Upper Incomplete Unit Gamma Function (Γ(z,x) / Γ(z))
- chk : Incomplete Gamma Function Check Value (= 1)
- ln(Γ(z)) : Log Gamma Function
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CALCULATOR : Lower Incomplete Gamma Unit Function [FREE] ±
Calculate the lower incomplete Gamma unit function from z and x, or calculate the inverse function x from z and p. The inverse function calculates x such that P(z,x) = p. The inverse function is valid for 0 ≤ p ≤ 1. Tool Input- gztype : Gamma Function Type
- xu : User Defined Gamma x Value
- pu : User Defined Incomplete Gamma Unit Value
- z : Gamma z Value
Tool Output- p : Incomplete Gamma Unit Value
- x : Gamma x Value
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CALCULATOR : Upper Incomplete Gamma Unit Function [FREE] ±
Calculate the upper incomplete Gamma unit function from z and x, or calculate the inverse function x from z and p. The inverse function calculates x such that P(z,x) = p. The inverse function is valid for 0 ≤ p ≤ 1. Tool Input- gztype : Gamma Function Type
- xu : User Defined Gamma x Value
- pu : User Defined Incomplete Gamma Unit Value
- z : Gamma z Value
Tool Output- p : Incomplete Gamma Unit Value
- x : Gamma x Value
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