mpfr-special-functions {Rmpfr} | R Documentation |
Special Mathematical Functions, supported by the MPFR Library.
zeta(x) Ei(x) Li2(x) erf(x) erfc(x)
x |
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
.
A vector of the same length as x
, of class mpfr
.
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.
Note the (integer order, non modified) Bessel functions j_0(),
y_n(), etc, named j0, yn
etc, and Airy
function Ai() in Bessel_mpfr.
curve(Ei, 0, 5, n=2001) ## As we now require (mpfrVersion() >= "2.4.0"): 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)