Number-theoretical, combinatorial and integer functions

-------------------------------------------------------



For factorial-type functions, including binomial coefficients,

double factorials, etc., see the separate section of the documentation.





Fibonacci numbers

.................



:func:`fibonacci`/:func:`fib`

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

.. autofunction:: mpmath.functions.fibonacci(n, **kwargs)





Bernoulli numbers and polynomials

.................................



:func:`bernoulli`

^^^^^^^^^^^^^^^^^

.. autofunction:: mpmath.functions.bernoulli(n)



:func:`bernfrac`

^^^^^^^^^^^^^^^^^

.. autofunction:: mpmath.functions.bernfrac(n)



:func:`bernpoly`

^^^^^^^^^^^^^^^^^

.. autofunction:: mpmath.functions.bernpoly(n,z)





Bell numbers and polynomials

...........................................



:func:`bell`

^^^^^^^^^^^^^^^^^

.. autofunction:: mpmath.functions.bell(n,x)





Prime counting functions

........................



:func:`primepi`

^^^^^^^^^^^^^^^^^

.. autofunction:: mpmath.functions.primepi(x)



:func:`primepi2`

^^^^^^^^^^^^^^^^^

.. autofunction:: mpmath.functions.primepi2(x)



:func:`riemannr`

^^^^^^^^^^^^^^^^^

.. autofunction:: mpmath.functions.riemannr(x)





Cyclotomic polynomials

......................



:func:`cyclotomic`

^^^^^^^^^^^^^^^^^^

.. autofunction:: mpmath.functions.cyclotomic(n,x)