TITLE(Special @@ Special Functions of Mathematics)
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)
)
ALIAS(beta)
ALIAS(lbeta)
ALIAS(gamma)
ALIAS(lgamma)
ALIAS(digamma)
ALIAS(trigamma)
ALIAS(tetragamma)
ALIAS(pentagamma)
ALIAS(choose)
ALIAS(lchoose)
DESCRIPTION(
The functions LANG(beta) and LANG(lbeta) return the beta function
and the natural logarithm of the beta function.
PARA
The functions LANG(gamma) and LANG(lgamma) return the gamma function
and the natural logarithm of the gamma function.
PARA
The functions LANG(digamma), LANG(trigamma), LANG(tetragamma) and
LANG(pentagamma)
return the first, second, third and fourth derivatives of the logarithm
of the gamma function.
PARA
The functions LANG(choose) and LANG(lchoose)
return binomial coefficients and
their logarithms.
)
EXAMPLES(
choose(5,2)
for(n in 0:10) print(choose(n,k = 0:n))
BLANK
x <- seq(.1, 4, length=201); dx <- diff(x)[1]
par(mfrow=c(2,3))
for(ch in c("", "l","di","tri","tetra","penta")) {
	deriv <- nchar(ch)>=2;  if(deriv) dy <- diff(y) / dx
	nm <- paste(ch,"gamma",sep=''); y <- get(nm)(x)
	plot(x, y, type='l', main=nm, col=1)
	abline(h=0,col="lightgray")
	if(deriv) lines(x[-1], dy, col=2, lty=2)
}
par(mfrow=c(2,2))
)
