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Special mathematical functions in Julia, include 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.

...The well-optimized DifferentialEquations solvers benchmark as some of the fastest implementations, using classic algorithms and ones from recent research which routinely outperform the “standard” C/Fortran methods, and include algorithms optimized for high-precision and HPC applications. At the same time, it wraps the classic C/Fortran methods, making it easy to switch over to them whenever necessary. Solving differential equations with different methods from different languages and packages can be done by changing one line of code, allowing for easy benchmarking to ensure you are using the fastest method possible.

...The well-optimized DifferentialEquations solvers benchmark as some of the fastest implementations, using classic algorithms and ones from recent research that routinely outperform the “standard” C/Fortran methods, and include algorithms optimized for high-precision and HPC applications. At the same time, it wraps the classic C/Fortran methods, making it easy to switch over to them whenever necessary. Solving differential equations with different methods from different languages and packages can be done by changing one line of code, allowing for easy benchmarking to ensure you are using the fastest method possible.

Statistics and stochastic calculus for Markov processes in continuous time, include univariate and multivariate stochastic processes such as stochastic differential equations or diffusions (SDE's) or Levy processes.