‘✓’ indicates that a software package implements the functions in a section;‘a’ indicates available functionality through optional or add-on packages;an empty space indicates no known support.
In the list below we identify four main sources of software for computing special functions.Please see ourSoftware Indexing Policy for rules that govern the indexing ofsoftware in the DLMF.
This is software of narrow scope developed as a byproductof a research project and subsequently made available at no cost to the public.The software is often meant to demonstrate new numerical methods or softwareengineering strategies which were the subject of a research project. Whendeveloped, the software typically contains capabilities unavailable elsewhere.While the software may be quite capable, it is typically not professionallypackaged and its use may require some expertise. The software is typicallyprovided as source code or via a web-based service, and no support is provided.
These are collections of software (e.g. libraries) or interactive systems ofa somewhat broad scope. Contents may be adapted from research software or maybe contributed by project participants who donate their services to the project.The software is made freely available to the public, typically in source code form.While formal support of the collection may not be provided by its developers,within active projects there is often a core group whodonate time to consider bug reports and make updates to the collection.
An increasing number of published books haveincluded digital media containing software described in the book. Often, thecollection of software covers a fairly broad area. Such software is typicallydeveloped by the book author. While it is not professionally packaged,it often provides a useful tool for readers to experiment with the conceptsdiscussed in the book. The software itself is typically not formally supportedby its authors.
Such software ranges from a collection of reusable softwareparts (e.g., a library) to fully functional interactive computing environmentswith an associated computing language. Such software is usually professionallydeveloped, tested, and maintained to high standards. It is available for purchase,often with accompanying updates and consulting support.
The following are web-based software repositories with significant holdings in thearea of special functions. Many research software packages are found here, as wellas some open source software collections.
Software published by the journal ACMTransactions on Mathematical Software(TOMS).
Software associated with papers published in the journalComputer PhysicsCommunications.
A collection of mathematical software, papers, and databases produced bythe numerical analysis research community.
A cross index of mathematical software in use at NIST.