MyCalcBuddy

Gamma Function Calculator

Calculate gamma function Ξ“(z), log-gamma, digamma, and trigamma functions.

Function Parameters

Gamma Function Definition

Ξ“(z) = βˆ«β‚€^∞ t^(z-1) e^(-t) dt

For positive integers: Ξ“(n) = (n-1)!

Quick Values

Special Values

Ξ“(1/2) = βˆšΟ€1.772454
Ξ“(1) = 11.000000
Ξ“(3/2) = βˆšΟ€/20.886227
Ξ“(2) = 11.000000
Ξ“(5/2) = 3βˆšΟ€/41.329340

Gamma Function Ξ“(5)

2.40000000e+1

= (4)!

Log Gamma ln(Ξ“)

3.178054

Digamma ψ(z)

1.506118

Trigamma ψ'(z)

0.225160

Gamma for Integers

Ξ“(1) = 0!1
Ξ“(2) = 1!1
Ξ“(3) = 2!2
Ξ“(4) = 3!6
Ξ“(5) = 4!24
Ξ“(6) = 5!120
Ξ“(7) = 6!720
Ξ“(8) = 7!5040
Ξ“(9) = 8!40320
Ξ“(10) = 9!362880

Properties

  • β€’ Ξ“(z+1) = zΒ·Ξ“(z)
  • β€’ Ξ“(n) = (n-1)! for integers
  • β€’ Ξ“(1/2) = βˆšΟ€
  • β€’ ψ(z) = d/dz ln(Ξ“(z))