Rmpfr (version 0.5-3)

mpfr-special-functions: Special Mathematical Functions (MPFR)

Description

Special Mathematical Functions, supported by the MPFR Library.

Usage

zeta(x)
Ei(x)
Li2(x)
erf(x)
erfc(x)
pnorm(q, mean = 0, sd = 1, lower.tail = TRUE, log.p = FALSE)

Arguments

x, q,mean,sd

a numeric or mpfr vector.

lower.tail, log.p

logical, see pnorm (or other p*() functions).

Value

• A vector of the same length as x, of class mpfr.

Details

zeta(x) computes Riemann's Zeta function $\zeta(x)$ important in analytical number theory and related fields. The traditional definition is $$\zeta(x) = \sum_{n=1}^\infty \frac{1}{n^x}.$$

Ei(x) computes the exponential integral, $$\int_{-\infty}^{x} \frac{e^t}{t} \; dt.$$

Li2(x) computes the dilogarithm, $$\int_{0}^{x} \frac{-log(1-t)}{t} \; dt.$$

erf(x) and erfc(x) are the error, respectively complementary error function which are both reparametrizations of pnorm, erf(x) = 2*pnorm(sqrt(2)*x) and erfc(x) = 2* pnorm(sqrt(2)*x, lower=FALSE).

See Also

pnorm in standard package stats; the class description mpfr mentioning the generic arithmetic and mathematical functions (sin, log, ..., etc) for which "mpfr" methods are available.

Examples

curve(Ei,  0, 5, n=2001)

if(mpfrVersion() >= "2.4.0") { ## Li2() is not available in older MPFR versions
curve(Li2, 0, 5, n=2001)

curve(Li2, -2, 13,   n=2000); abline(h=0,v=0, lty=3)
curve(Li2, -200,400, n=2000); abline(h=0,v=0, lty=3)
}

curve(erf, -3,3, col = "red", ylim = c(-1,2))
curve(erfc, add = TRUE, col = "blue")
abline(h=0, v=0, lty=3)
legend(-3,1, c("erf(x)", "erfc(x)"), col = c("red","blue"), lty=1)