HP 50g User Manual page 145

GAMMA:
PSI:
Psi:
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
Therefore, it can be related to the factorial of a number, i.e.,
when is a positive integer. We can also use the factorial function to calculate
the Gamma function, and vice versa. For example, (5) = 4! or,
4~‚2`. The factorial function is available in the MTH menu,
through the 7. PROBABILITY.. menu.
The PSI function,
( , )
i.e., n x
Psi function. For this function, y must be a positive integer.
The Psi function,
The Gamma function ( )
N-th derivative of the digamma function
Digamma function, derivative of the ln(Gamma)
(x,y), represents the y-th derivative of the digamma function,
n
d
( )
x , where
n
dx
(x), or digamma function, is defined as
∫
1
( )
x
0
, for > 1.
(x) is known as the digamma function, or
x
e dx
. This function has
( x ) ln[ ( x )]
.
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