chore: import upstream snapshot with attribution

2026-07-13 12:32:53 +08:00
commit 2a16f2f53b
247 changed files with 69150 additions and 0 deletions
@@ -0,0 +1,70 @@
+Exponential integrals and error functions
+-----------------------------------------
+
+Exponential integrals give closed-form solutions to a large class of commonly
+occurring transcendental integrals that cannot be evaluated using elementary
+functions.  Integrals of this type include those with an integrand of the form
+`t^a e^{t}` or `e^{-x^2}`, the latter giving rise to the Gaussian (or normal)
+probability distribution.
+
+The most general function in this section is the incomplete gamma function, to
+which all others can be reduced.  The incomplete gamma function, in turn, can
+be expressed using hypergeometric functions (see :doc:`hypergeometric`).
+
+Incomplete gamma functions
+..........................
+
+.. autofunction:: mpmath.gammainc
+.. autofunction:: mpmath.lower_gamma
+.. autofunction:: mpmath.upper_gamma
+
+
+Exponential integrals
+.....................
+
+.. autofunction:: mpmath.ei
+.. autofunction:: mpmath.e1
+.. autofunction:: mpmath.expint
+
+
+Logarithmic integral
+....................
+
+.. autofunction:: mpmath.li
+
+
+Trigonometric integrals
+.......................
+
+.. autofunction:: mpmath.ci
+.. autofunction:: mpmath.si
+
+
+Hyperbolic integrals
+....................
+
+.. autofunction:: mpmath.chi
+.. autofunction:: mpmath.shi
+
+
+Error functions
+...............
+
+.. autofunction:: mpmath.erf
+.. autofunction:: mpmath.erfc
+.. autofunction:: mpmath.erfi
+.. autofunction:: mpmath.erfinv
+
+
+The normal distribution
+.......................
+
+.. autofunction:: mpmath.npdf
+.. autofunction:: mpmath.ncdf
+
+
+Fresnel integrals
+.................
+
+.. autofunction:: mpmath.fresnels
+.. autofunction:: mpmath.fresnelc