6.8.13  The Γ function: Gamma

The Gamma function is defined by

If x is a positive integer, Γ is computed by applying the recurrence:

Hence:

and the Gamma function is used to generalize the factorial (see Section 6.6.1).

The Gamma command computes the Gamma function.

• Gamma takes one argument:
  a, a number.
• Gamma(a) returns the value Γ(a).

Examples.

• Input:
  Gamma(5)
  Output:

  24

• Input:
  Gamma(0.7)
  Output:

  1.29805533265

• Input:
  Gamma(-0.3)
  Output:

  −4.32685110883

  Indeed: Gamma(0.7)=-0.3*Gamma(-0.3)
  
• Input:
  Gamma(-1.3)
  Output:

  3.32834700679

  Indeed Gamma(0.7)=-0.3*Gamma(-0.3)=(-0.3)*(-1.3)*Gamma(-1.3)