RICA

Short Description

The RICA (Rule Induced Convolutions for Asymptotics) package by Nikolai Fadeev, which aims at calculating Mellin representations and asymptotic expansions at infinity of binomially weighted sums.

Licence

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see https://www.gnu.org/licenses.

The Package

The package can be downloaded here:

• RICA.m   

We note that in order to use RICA, one should load beforehand the Sigma package by Carsten Schneider and the HarmonicSums package by Jakob Ablinger. Here below is a Mathematica notebook presenting some examples of usage of RICA:

• Examples_RICA.nb   

Right now you are using Version 1.0 released in July, 2025. Please report any bugs and comments to Nikolai Fadeev. A currently maintained version is available at RISC, contact Carsten Schneider.

Literature

More information about the package can be found in

• J. Blümlein, N. Fadeev and C. Schneider. Computing Mellin representations and asymptotics of nested binomial sums in a symbolic way: the RICA package. ACM Communications in Computer Algebra, Vol. 57, No. 2, Issue 224, June 2023 [url]