Module peroxide::special

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Special functions module

This module provides implementations of various special mathematical functions commonly used in statistical and scientific computing. It includes:

  • Basic special functions:

    • Gaussian (Normal) function
    • Gamma function and its logarithm
    • Pochhammer symbol (rising factorial)

  • Incomplete special functions:

    • Regularized incomplete gamma function and its inverse
    • Regularized incomplete beta function and its inverse

  • Error functions:

    • Error function (erf) and its complement (erfc)
    • Inverse error function and inverse complementary error function

  • Other functions:

    • Beta function
    • Phi function (CDF of the standard normal distribution)
    • Lambert W function (principal branch W₀ and secondary branch W₋₁)

Many of these functions are implemented using efficient numerical approximations or by wrapping functions from other crates (e.g., puruspe).

The module also includes an enum LambertWAccuracyMode to control the accuracy-speed trade-off for Lambert W function calculations.

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