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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
       loaded.
       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
       Performance is quite bad.

SEE ALSO
       Math::Prime::Util

       Math::Prime::Util::GMP

       Math::MPFR

       Math::Pari

AUTHORS
       Dana Jacobsen <dana@acm.org>

COPYRIGHT
       Copyright 2012 by Dana Jacobsen <dana@acm.org>

       This program is free software; you can redistribute it and/or modify it
       under the same terms as Perl itself.

perl v5.32.1			  2018-11-15Math::Prime::Util::ZetaBigFloat(3)

NAME | VERSION | SYNOPSIS | DESCRIPTION | FUNCTIONS | LIMITATIONS | PERFORMANCE | SEE ALSO | AUTHORS | COPYRIGHT

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