# HP 48gII User Manual Page 140

Graphing calculator.

The Gamma function Γ(α)
GAMMA:
PSI:
N-th derivative of the digamma function
Psi:
Digamma function, derivative of the ln(Gamma)
The Gamma function is defined by
applications in applied mathematics for science and engineering, as well as
in probability and statistics.
Factorial of a number
The factorial of a positive integer number n is defined as n!=n⋅(n-1)⋅(n-
2) ...3⋅2⋅1, with 0! = 1. The factorial function is available in the calculator by
using ~‚2. In both ALG and RPN modes, enter the number first,
followed by the sequence ~‚2. Example: 5~‚2`.
The Gamma function, defined above, has the property that
Γ(α) = (α−1) Γ(α−1), for α > 1.
Therefore, it can be related to the factorial of a number, i.e., Γ(α) = (α−1)!,
when α is a positive integer. We can also use the factorial function to
calculate the Gamma function, and vice versa. For example, Γ(5) = 4! or,
4~‚2`. The factorial function is available in the MTH menu,
The PSI function, Ψ(x,y), represents the y-th derivative of the digamma function,
n
d
(
,
)
ψ
(
n
x
i.e.,
n
dx
Psi function. For this function, y must be a positive integer.
The Psi function, ψ(x), or digamma function, is defined as
(
α
)
0
)
, where ψ(x) is known as the digamma function, or
x
α
1
x
x
e
dx
. This function has
ψ
(
x
)
ln[
(
Page 3-15
x
)]
.