HP 48gII Graphing Calculator Manual do Utilizador descarregar pdf (Página 140)

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GAMMA: The Gamma function Γ(α)

PSI: N-th derivative of the digamma function

Psi: Digamma function, derivative of the ln(Gamma)

The Gamma function

is defined by

∫

∞

−−

=Γ

)( dxex

xα

α . This function has

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,

through the 7. PROBABILITY.. menu.

The PSI function

, Ψ(x,y), represents the y-th derivative of the digamma function,

i.e.,

)(),( x

ψ=Ψ , where ψ(x) is known as the digamma function, or

Psi function. For this function, y must be a positive integer.

The Psi function

, ψ(x), or digamma function, is defined as )](ln[)( xx Γ=

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