zef:FRITH

# NAME

Math::Libgsl::Series - An interface to libgsl, the Gnu Scientific Library - Series Acceleration

# SYNOPSIS

```use Math::Libgsl::Series;
```

# SYNOPSIS

```use Math::Libgsl::Series;

my Math::Libgsl::Series \$s .= new: N;
constant \N = 20;
my @array := Array[Num].new;
(^N).map: -> \$n { my \$np1 = \$n + 1e0; @array[\$n] = 1e0 / (\$np1 * \$np1) }
my (\$sum, \$err) = \$s.levin-accel: @array;
say "The series' sum is \$sum, with an estimated error \$err";
```

# DESCRIPTION

Math::Libgsl::Series is an interface to the Series Acceleration functions of libgsl, the Gnu Scientific Library.

### new(UInt:D() :\$size!, Bool :\$truncation? = False)

The constructor accepts one or optionally two simple or named arguments: the mandatory series size and the optional error estimation type. This last argoment may have two values: propagation of rounding error or truncation error in the estrapolation. If the Bool :\$truncation parameter is True then the error is estimated by means of the truncation error in the estrapolation. If the Bool :\$truncation parameter is False then the error is estimated by means of the propagation of rounding errors.

### levin-accel(*@array where *.all > 0 --> List)

This method computes the extrapolated limit of the series using a Levin u-transform. It returns a List: the extrapolated \$sum, the estimated \$error, and the number of \$terms-used during the computation.

# C Library Documentation

For more details on libgsl see https://www.gnu.org/software/gsl/. The excellent C Library manual is available here https://www.gnu.org/software/gsl/doc/html/index.html, or here https://www.gnu.org/software/gsl/doc/latex/gsl-ref.pdf in PDF format.

# Prerequisites

This module requires the libgsl library to be installed. Please follow the instructions below based on your platform:

## Debian Linux and Ubuntu 20.04+

``````sudo apt install libgsl23 libgsl-dev libgslcblas0
``````

That command will install libgslcblas0 as well, since it's used by the GSL.

## Ubuntu 18.04

libgsl23 and libgslcblas0 have a missing symbol on Ubuntu 18.04. I solved the issue installing the Debian Buster version of those three libraries:

# Installation

To install it using zef (a module management tool):

``````\$ zef install Math::Libgsl::Series
``````

# AUTHOR

Fernando Santagata nando.santagata@gmail.com