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Math::Prime::Util::ZetUserFContributed Perl Math::Prime::Util::ZetaBigFloat(3)

NAME
Math::Prime::Util::ZetaBigFloat - Perl Big Float	versions of Riemann
Zeta and	R functions

VERSION
Version 0.73

SYNOPSIS
Math::BigFloat versions`of the Riemann Zeta and Riemann R functions.
These are kept in a separate module because they	use a lot of big
tables that we'd	prefer to only load if needed.

DESCRIPTION
Pure Perl implementations of Riemann Zeta and Riemann R using
Math::BigFloat.	These functions	are used if:

The input is a BigInt, a	BigFloat, or the bignum	module has been
The Math::Prime::Util::GMP module is not	available or old.

If you use these	functions a lot, I highly recommend you	install
Math::Prime::Util::GMP, which the main Math::Prime::Util	functions will
find.  These give much better performance, and better accuracy.	You
can also	use Math::Pari and Math::MPFR for the Riemann Zeta function.

FUNCTIONS
RiemannZeta
my \$z = RiemannZeta(\$s);

Given a floating	point input "s"	where "s >= 0.5", returns the floating
point value of I<paragraph>(s)-1, where I<paragraph>(s) is the Riemann
zeta function.  One is subtracted to ensure maximum precision for large
values of "s".  The zeta	function is the	sum from k=1 to	infinity of "1
/ k^s"

Results are calculated using either Borwein (1991) algorithm 2, or the
basic series.  Full input accuracy is attempted,	but there are defects
in Math::BigFloat with high accuracy computations that make this
difficult.

RiemannR
my \$r = RiemannR(\$x);

Given a positive	non-zero floating point	input, returns the floating
point value of Riemann's	R function.  Riemann's R function gives	a very
close approximation to the prime	counting function.

Accuracy	should be about	35 digits.

LIMITATIONS
Bugs in Math::BigFloat (RT 43692, RT 77105) cause many problems with
this code.  I've	attempted to work around them, but it is possible
there are cases they miss.

The accuracy goals (35 digits) are sometimes missed by a	digit or two.

PERFORMANCE

Math::Prime::Util

Math::Prime::Util::GMP

Math::MPFR

Math::Pari

AUTHORS
Dana Jacobsen <dana@acm.org>