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Special Functions of Mathematics

Syntax

beta(a, b)
lbeta(a, b)
gamma(a)
lgamma(a)
digamma(a)
trigamma(a)
tetragamma(a)
pentagamma(a)
choose(n,k)
lchoose(n,k)

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.

Examples

choose(5,2) for(n in 0:10) print(choose(n,k = 0:n)) <P> 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) }