305 Stars
Updated Last
7 Months Ago
Started In
May 2016


Special mathematical functions in Julia, including Bessel, Hankel, Airy, error, Dawson, exponential (or sine and cosine) integrals, eta, zeta, digamma, inverse digamma, trigamma, and polygamma functions. Most of these functions were formerly part of Base in early versions of Julia.

CI (Linux, macOS, FreeBSD, Windows): CI codecov

Documentation: Documentation Documentation

Test status (most recent release): PkgEval

Upgrading from SpecialFunctions 1

SpecialFunctions 2 has only a single breaking change: The removal of the type piracy Base.factorial(x::Number) = gamma(x + 1). For most users this change will not break anything but for users of factorial it might. If you want to upgrade from SpecialFunctions 1 to SpecialFunctions 2 we recommend:

  • If your code does not use factorial then update the compat entry for SpecialFunctions to e.g. "1.8.1, 2".

  • If your code does use factorial then check for all occurrences of factorial:

    • If factorial is called on an Integer, keep factorial,
    • Otherwise replace factorial(x) with a call to gamma(x + 1).

    Afterwards update the compat entry for SpecialFunctions and check that your package works with SpecialFunctions 2.

As the previous overload of factorial was type piratical (added 4 years ago when code was moved out of Base), it is possible that you used it without a direct dependency on SpecialFunctions as long as SpecialFunctions was loaded. The package ecosystem was analyzed and this only impacted a couple of packages. However, it is possible that private packages that depend on this may need updating, or stay with the older release of SpecialFunctions.jl.