Special {base} | R Documentation |
Special Functions of Mathematics
Description
The functions beta
and lbeta
return the beta function
and the natural logarithm of the beta function.
The functions gamma
and lgamma
return the gamma function
and the natural logarithm of the gamma function.
The functions digamma
, trigamma
, tetragamma
and
pentagamma
return the first, second, third and fourth
derivatives of the logarithm of the gamma function.
The functions choose
and lchoose
return binomial
coefficients and their logarithms.
Usage
beta(a, b)
lbeta(a, b)
gamma(a)
lgamma(a)
digamma(a)
trigamma(a)
tetragamma(a)
pentagamma(a)
choose(n,k)
lchoose(n,k)
See Also
Arithmetic
for simple and Math
for miscellaneous
mathematical functions.
Examples
choose(5, 2)
for (n in 0:10) print(choose(n, k = 0:n))
x <- seq(.1, 4, length = 201); dx <- diff(x)[1]
par(mfrow = c(2, 3))
for (ch in c("", "l","di","tri","tetra","penta")) {
is.deriv <- nchar(ch) >= 2
if (is.deriv) dy <- diff(y) / dx
nm <- paste(ch, "gamma", sep = "")
y <- get(nm)(x)
plot(x, y, type = "l", main = nm, col = "red")
abline(h = 0, col = "lightgray")
if (is.deriv) lines(x[-1], dy, col = "blue", lty = 2)
}
par(mfrow = c(2, 2))