Functions to compute the gamma function, its logarithm, digamma, trigamma, polygamma, and various incomplete gamma functions.
Usage
tgamma(z)
tgamma1pm1(z)
lgamma_boost(z)
digamma_boost(z)
trigamma_boost(z)
polygamma(n, z)
tgamma_ratio(a, b)
tgamma_delta_ratio(a, delta)
gamma_p(a, z)
gamma_q(a, z)
tgamma_lower(a, z)
tgamma_upper(a, z)
gamma_q_inv(a, q)
gamma_p_inv(a, p)
gamma_q_inva(z, q)
gamma_p_inva(z, p)
gamma_p_derivative(a, z)Arguments
- z
Input numeric value for the gamma function
- n
Order of the polygamma function (non-negative integer)
- a
Argument for the incomplete gamma functions
- b
Denominator argument for the ratio of gamma functions
- delta
Increment for the ratio of gamma functions
- q
Probability value for the incomplete gamma functions
- p
Probability value for the incomplete gamma functions
Value
A single numeric value with the computed gamma function, logarithm, digamma, trigamma, polygamma, or incomplete gamma functions.
See also
Boost Documentation for more details on the mathematical background.
Examples
if (FALSE) { # \dontrun{
# Gamma function for z = 5
tgamma(5)
# Gamma function for (1 + z) - 1, where z = 5
tgamma1pm1(5)
# Logarithm of the gamma function for z = 5
lgamma_boost(5)
# Digamma function for z = 5
digamma_boost(5)
# Trigamma function for z = 5
trigamma_boost(5)
# Polygamma function of order 1 for z = 5
polygamma(1, 5)
# Ratio of gamma functions for a = 5, b = 3
tgamma_ratio(5, 3)
# Ratio of gamma functions with delta for a = 5, delta = 2
tgamma_delta_ratio(5, 2)
# Normalised lower incomplete gamma function P(a, z) for a = 5, z = 2
gamma_p(5, 2)
# Normalised upper incomplete gamma function Q(a, z) for a = 5, z = 2
gamma_q(5, 2)
# Full lower incomplete gamma function for a = 5, z = 2
tgamma_lower(5, 2)
# Full upper incomplete gamma function for a = 5, z = 2
tgamma_upper(5, 2)
# Inverse of the normalised upper incomplete gamma function for a = 5, q = 0.5
gamma_q_inv(5, 0.5)
# Inverse of the normalised lower incomplete gamma function for a = 5, p = 0.5
gamma_p_inv(5, 0.5)
# Inverse of the normalised upper incomplete gamma function with respect to a for z = 2, q = 0.5
gamma_q_inva(2, 0.5)
# Inverse of the normalised lower incomplete gamma function with respect to a for z = 2, p = 0.5
gamma_p_inva(2, 0.5)
# Derivative of the normalised upper incomplete gamma function for a = 5, z = 2
gamma_p_derivative(5, 2)
} # }