diff --git a/Doc/library/math.rst b/Doc/library/math.rst index ec3955dabfb..a5be90ede30 100644 --- a/Doc/library/math.rst +++ b/Doc/library/math.rst @@ -156,10 +156,10 @@ Power and logarithmic functions .. function:: expm1(x) - Return ``e**x - 1``. For small floats *x*, the subtraction in - ``exp(x) - 1`` can result in a significant loss of precision; the - :func:`expm1` function provides a way to compute this quantity to - full precision:: + Return ``e**x - 1``. For small floats *x*, the subtraction in ``exp(x) - 1`` + can result in a `significant loss of precision + `_\; the :func:`expm1` + function provides a way to compute this quantity to full precision:: >>> from math import exp, expm1 >>> exp(1e-5) - 1 # gives result accurate to 11 places @@ -269,6 +269,9 @@ Angular conversion Hyperbolic functions -------------------- +`Hyperbolic functions `_ +are analogs of trigonometric functions that are based on hyperbolas +instead of circles. .. function:: acosh(x) @@ -305,21 +308,34 @@ Special functions .. function:: erf(x) - Return the error function at *x*. + Return the `error function `_ at + *x*. + + The :func:`erf` function can be used to compute traditional statistical + functions such as the `cumulative standard normal distribution + `_:: + + def phi(x): + 'Cumulative distribution function for the standard normal distribution' + return (1.0 + erf(x / sqrt(2.0))) / 2.0 .. versionadded:: 3.2 .. function:: erfc(x) - Return the complementary error function at *x*. + Return the complementary error function at *x*. The `complementary error + function `_ is defined as + ``1.0 - erf(x)``. It is used for large values of *x* where a straight + substraction from *1* would cause a `loss of significance + `_\. .. versionadded:: 3.2 .. function:: gamma(x) - Return the Gamma function at *x*. + Return the `Gamma function` at *x*. .. versionadded:: 3.2