boostmath (version 1.0.0)

gamma_functions: Gamma Functions

Description

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)

Value

A single numeric value with the computed gamma function, logarithm, digamma, trigamma, polygamma, or incomplete gamma functions.

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

See Also

Boost Documentation for more details on the mathematical background.

Examples

if (FALSE) {
# 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)
}