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Zeta functions, L-series and polylogarithms
-------------------------------------------
This section includes the Riemann zeta functions
and associated functions pertaining to analytic number theory.
Riemann and Hurwitz zeta functions
..................................................
:func:`zeta`
^^^^^^^^^^^^^^^^^
.. autofunction:: mpmath.zeta(s,a=1,derivative=0)
Dirichlet L-series
..................................................
:func:`altzeta`
^^^^^^^^^^^^^^^
.. autofunction:: mpmath.altzeta(s)
:func:`dirichlet`
^^^^^^^^^^^^^^^^^^
.. autofunction:: mpmath.dirichlet(s,chi,derivative=0)
Stieltjes constants
...................
:func:`stieltjes`
^^^^^^^^^^^^^^^^^
.. autofunction:: mpmath.stieltjes(n,a=1)
Zeta function zeros
......................................
These functions are used for the study of the Riemann zeta function
in the critical strip.
:func:`zetazero`
^^^^^^^^^^^^^^^^
.. autofunction:: mpmath.zetazero(n, verbose=False)
:func:`nzeros`
^^^^^^^^^^^^^^^^
.. autofunction:: mpmath.nzeros(t)
:func:`siegelz`
^^^^^^^^^^^^^^^^^
.. autofunction:: mpmath.siegelz(t)
:func:`siegeltheta`
^^^^^^^^^^^^^^^^^^^
.. autofunction:: mpmath.siegeltheta(t)
:func:`grampoint`
^^^^^^^^^^^^^^^^^
.. autofunction:: mpmath.grampoint(n)
:func:`backlunds`
^^^^^^^^^^^^^^^^^
.. autofunction:: mpmath.backlunds(t)
Lerch transcendent
................................
:func:`lerchphi`
^^^^^^^^^^^^^^^^
.. autofunction:: mpmath.lerchphi(z,s,a)
Polylogarithms and Clausen functions
.......................................
:func:`polylog`
^^^^^^^^^^^^^^^
.. autofunction:: mpmath.polylog(s,z)
:func:`clsin`
^^^^^^^^^^^^^^^^^
.. autofunction:: mpmath.clsin(s, z)
:func:`clcos`
^^^^^^^^^^^^^^^^^
.. autofunction:: mpmath.clcos(s, z)
:func:`polyexp`
^^^^^^^^^^^^^^^^^
.. autofunction:: mpmath.polyexp(s,z)
Zeta function variants
..........................
:func:`primezeta`
^^^^^^^^^^^^^^^^^
.. autofunction:: mpmath.primezeta(s)
:func:`secondzeta`
^^^^^^^^^^^^^^^^^^
.. autofunction:: mpmath.secondzeta(s, a=0.015, **kwargs)
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