class_docstr: Hurwitz zeta function (or Riemann zeta function).
  
  Explanation
  ===========
  
  For $\operatorname{Re}(a) > 0$ and $\operatorname{Re}(s) > 1$, this
  function is defined as
  
  .. math:: \zeta(s, a) = \sum_{n=0}^\infty \frac{1}{(n + a)^s},
  
  where the standard choice of argument for $n + a$ is used. For fixed
  $a$ not a nonpositive integer the Hurwitz zeta function admits a
  meromorphic continuation to all of $\mathbb{C}$; it is an unbranched
  function with a simple pole at $s = 1$.
  
  The Hurwitz zeta function is a special case of the Lerch transcendent:
  
  .. math:: \zeta(s, a) = \Phi(1, s, a).
  
  This formula defines an analytic continuation for all possible values of
  $s$ and $a$ (also $\operatorname{Re}(a) < 0$), see the documentation of
  :class:`lerchphi` for a description of the branching behavior.
  
  If no value is passed for $a$ a default value of $a = 1$ is assumed,
  yielding the Riemann zeta function.
  
  Examples
  ========
  
  For $a = 1$ the Hurwitz zeta function reduces to the famous Riemann
  zeta function:
  
  .. math:: \zeta(s, 1) = \zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s}.
  
  >>> from sympy import zeta
  >>> from sympy.abc import s
  >>> zeta(s, 1)
  zeta(s)
  >>> zeta(s)
  zeta(s)
  
  The Riemann zeta function can also be expressed using the Dirichlet eta
  function:
  
  >>> from sympy import dirichlet_eta
  >>> zeta(s).rewrite(dirichlet_eta)
  dirichlet_eta(s)/(1 - 2**(1 - s))
  
  The Riemann zeta function at nonnegative even and negative integer
  values is related to the Bernoulli numbers and polynomials:
  
  >>> zeta(2)
  pi**2/6
  >>> zeta(4)
  pi**4/90
  >>> zeta(0)
  -1/2
  >>> zeta(-1)
  -1/12
  >>> zeta(-4)
  0
  
  The specific formulae are:
  
  .. math:: \zeta(2n) = -\frac{(2\pi i)^{2n} B_{2n}}{2(2n)!}
  .. math:: \zeta(-n,a) = -\frac{B_{n+1}(a)}{n+1}
  
  No closed-form expressions are known at positive odd integers, but
  numerical evaluation is possible:
  
  >>> zeta(3).n()
  1.20205690315959
  
  The derivative of $\zeta(s, a)$ with respect to $a$ can be computed:
  
  >>> from sympy.abc import a
  >>> zeta(s, a).diff(a)
  -s*zeta(s + 1, a)
  
  However the derivative with respect to $s$ has no useful closed form
  expression:
  
  >>> zeta(s, a).diff(s)
  Derivative(zeta(s, a), s)
  
  The Hurwitz zeta function can be expressed in terms of the Lerch
  transcendent, :class:`~.lerchphi`:
  
  >>> from sympy import lerchphi
  >>> zeta(s, a).rewrite(lerchphi)
  lerchphi(1, s, a)
  
  See Also
  ========
  
  dirichlet_eta, lerchphi, polylog
  
  References
  ==========
  
  .. [1] https://dlmf.nist.gov/25.11
  .. [2] https://en.wikipedia.org/wiki/Hurwitz_zeta_function
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code: def _eval_is_finite(self):
      arg_is_one = (self.args[0] - 1).is_zero
      if arg_is_one is not None:
          return not arg_is_one
  
imports: from sympy.core.add import Add
  from sympy.core.cache import cacheit
  from sympy.core.function import ArgumentIndexError, expand_mul, Function
  from sympy.core.numbers import pi, I, Integer
  from sympy.core.relational import Eq
  from sympy.core.singleton import S
  from sympy.core.symbol import Dummy
  from sympy.core.sympify import sympify
  from sympy.functions.combinatorial.numbers import bernoulli, factorial, genocchi, harmonic
  from sympy.functions.elementary.complexes import re, unpolarify, Abs, polar_lift
  from sympy.functions.elementary.exponential import log, exp_polar, exp
  from sympy.functions.elementary.integers import ceiling, floor
  from sympy.functions.elementary.miscellaneous import sqrt
  from sympy.functions.elementary.piecewise import Piecewise
  from sympy.polys.polytools import Poly
label_desc: Use image node_id 5 for calling the zeta obj's underlying member method code with example usage: obj._eval_is_finite() and returns: unknown