wehub-resource-sync
68 lines
1.6 KiB
ReStructuredText
68 lines
1.6 KiB
ReStructuredText
Sums, products, limits and extrapolation
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----------------------------------------
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The functions listed here permit approximation of infinite
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sums, products, and other sequence limits.
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Use :func:`mpmath.fsum` and :func:`mpmath.fprod`
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for summation and multiplication of finite sequences.
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Summation
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..........................................
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:func:`~mpmath.nsum`
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^^^^^^^^^^^^^^^^^^^^^
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.. autofunction:: mpmath.nsum
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:func:`~mpmath.sumem`
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^^^^^^^^^^^^^^^^^^^^^
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.. autofunction:: mpmath.sumem
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:func:`~mpmath.sumap`
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^^^^^^^^^^^^^^^^^^^^^
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.. autofunction:: mpmath.sumap
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Products
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...............................
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:func:`~mpmath.nprod`
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^^^^^^^^^^^^^^^^^^^^^^
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.. autofunction:: mpmath.nprod
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Limits (``limit``)
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..................
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:func:`~mpmath.limit`
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^^^^^^^^^^^^^^^^^^^^^^
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.. autofunction:: mpmath.limit
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Extrapolation
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..........................................
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The following functions provide a direct interface to
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extrapolation algorithms. :func:`~mpmath.nsum` and :func:`~mpmath.limit`
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essentially work by calling the following functions with an increasing
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number of terms until the extrapolated limit is accurate enough.
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The following functions may be useful to call directly if the
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precise number of terms needed to achieve a desired accuracy is
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known in advance, or if one wishes to study the convergence
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properties of the algorithms.
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:func:`~mpmath.richardson`
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^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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.. autofunction:: mpmath.richardson
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:func:`~mpmath.shanks`
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^^^^^^^^^^^^^^^^^^^^^^^
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.. autofunction:: mpmath.shanks
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:func:`~mpmath.levin`
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^^^^^^^^^^^^^^^^^^^^^^
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.. autofunction:: mpmath.levin
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:func:`~mpmath.cohen_alt`
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^^^^^^^^^^^^^^^^^^^^^^^^^^
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.. autofunction:: mpmath.cohen_alt
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