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71 lines
1.6 KiB
ReStructuredText
71 lines
1.6 KiB
ReStructuredText
Exponential integrals and error functions
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Exponential integrals give closed-form solutions to a large class of commonly
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occurring transcendental integrals that cannot be evaluated using elementary
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functions. Integrals of this type include those with an integrand of the form
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`t^a e^{t}` or `e^{-x^2}`, the latter giving rise to the Gaussian (or normal)
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probability distribution.
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The most general function in this section is the incomplete gamma function, to
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which all others can be reduced. The incomplete gamma function, in turn, can
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be expressed using hypergeometric functions (see :doc:`hypergeometric`).
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Incomplete gamma functions
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..........................
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.. autofunction:: mpmath.gammainc
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.. autofunction:: mpmath.lower_gamma
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.. autofunction:: mpmath.upper_gamma
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Exponential integrals
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.....................
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.. autofunction:: mpmath.ei
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.. autofunction:: mpmath.e1
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.. autofunction:: mpmath.expint
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Logarithmic integral
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....................
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.. autofunction:: mpmath.li
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Trigonometric integrals
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.......................
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.. autofunction:: mpmath.ci
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.. autofunction:: mpmath.si
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Hyperbolic integrals
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....................
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.. autofunction:: mpmath.chi
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.. autofunction:: mpmath.shi
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Error functions
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...............
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.. autofunction:: mpmath.erf
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.. autofunction:: mpmath.erfc
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.. autofunction:: mpmath.erfi
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.. autofunction:: mpmath.erfinv
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The normal distribution
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.......................
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.. autofunction:: mpmath.npdf
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.. autofunction:: mpmath.ncdf
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Fresnel integrals
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.................
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.. autofunction:: mpmath.fresnels
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.. autofunction:: mpmath.fresnelc
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