special-math: Special Mathematical Functions (MPFR)

Description Usage Arguments Details Value See Also Examples

Description

Special Mathematical Functions, supported by the MPFR Library.

Usage

1
2
3
4
5
6
zeta(x)
Ei(x)
Li2(x)

erf(x)
erfc(x)

Arguments

x

a numeric or mpfr vector.

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..Inf; 1/(n^x)].

Ei(x) computes the exponential integral,

Integral(-Inf,x; e^t/t dt).

Li2(x) computes the dilogarithm,

Integral(0,x; -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), and hence Rmpfr provides its own version of pnorm.

Value

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

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

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
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)

Rmpfr documentation built on Aug. 19, 2018, 3 a.m.