gaussratiovegind (version 2.0.3)

lnpochhammer: Logarithm of the Pochhammer Symbol

Description

Computes the logarithm of the Pochhammer symbol.

Usage

lnpochhammer(x, n)

Value

Numeric value. The logarithm of the Pochhammer symbol.

Arguments

x

numeric.

n

positive integer.

Author

Pierre Santagostini, Nizar Bouhlel

Details

The Pochhammer symbol is given by: $$ \displaystyle{ (x)_n = \frac{\Gamma(x+n)}{\Gamma(x)} = x (x+1) ... (x+n-1) } $$ So, if \(n > 0\): $$ \displaystyle{ log\left((x)_n\right) = log(x) + log(x+1) + ... + log(x+n-1) } $$

If \(n = 0\), \(\displaystyle{ log\left((x)_n\right) = log(1) = 0}\)

See Also

pochhammer, kummer

Examples

lnpochhammer(2, 0)
lnpochhammer(2, 1)
lnpochhammer(2, 3)