Description Usage Arguments Details Value See Also Examples

Special Mathematical Functions, supported by the MPFR Library.

1 2 3 4 5 6 |

`x` |
a |

`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 **e**xponential 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
**c**omplementary 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.

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)
``` |

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