class_docstr: Represents Finite Fourier sine/cosine series.
  
  For how to compute Fourier series, see the :func:`fourier_series`
  docstring.
  
  Parameters
  ==========
  
  f : Expr
      Expression for finding fourier_series
  
  limits : ( x, start, stop)
      x is the independent variable for the expression f
      (start, stop) is the period of the fourier series
  
  exprs: (a0, an, bn) or Expr
      a0 is the constant term a0 of the fourier series
      an is a dictionary of coefficients of cos terms
       an[k] = coefficient of cos(pi*(k/L)*x)
      bn is a dictionary of coefficients of sin terms
       bn[k] = coefficient of sin(pi*(k/L)*x)
  
      or exprs can be an expression to be converted to fourier form
  
  Methods
  =======
  
  This class is an extension of FourierSeries class.
  Please refer to sympy.series.fourier.FourierSeries for
  further information.
  
  See Also
  ========
  
  sympy.series.fourier.FourierSeries
  sympy.series.fourier.fourier_series
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code: def __new__(cls, f, limits, exprs):
      f = sympify(f)
      limits = sympify(limits)
      exprs = sympify(exprs)
  
      if not (
          isinstance(exprs, Tuple) and len(exprs) == 3
      ):  # exprs is not of form (a0, an, bn)
          # Converts the expression to fourier form
          c, e = exprs.as_coeff_add()
          from sympy.simplify.fu import TR10
  
          rexpr = c + Add(*[TR10(i) for i in e])
          a0, exp_ls = rexpr.expand(
              trig=False, power_base=False, power_exp=False, log=False
          ).as_coeff_add()
  
          x = limits[0]
          L = abs(limits[2] - limits[1]) / 2
  
          a = Wild(
              "a",
              properties=[
                  lambda k: k.is_Integer,
                  lambda k: k is not S.Zero,
              ],
          )
          b = Wild(
              "b",
              properties=[
                  lambda k: x not in k.free_symbols,
              ],
          )
  
          an = {}
          bn = {}
  
          # separates the coefficients of sin and cos terms in dictionaries an, and bn
          for p in exp_ls:
              t = p.match(b * cos(a * (pi / L) * x))
              q = p.match(b * sin(a * (pi / L) * x))
              if t:
                  an[t[a]] = t[b] + an.get(t[a], S.Zero)
              elif q:
                  bn[q[a]] = q[b] + bn.get(q[a], S.Zero)
              else:
                  a0 += p
  
          exprs = Tuple(a0, an, bn)
  
      return Expr.__new__(cls, f, limits, exprs)
  
imports: from sympy.core.numbers import oo, pi
  from sympy.core.symbol import Wild
  from sympy.core.expr import Expr
  from sympy.core.add import Add
  from sympy.core.containers import Tuple
  from sympy.core.singleton import S
  from sympy.core.symbol import Dummy, Symbol
  from sympy.core.sympify import sympify
  from sympy.functions.elementary.trigonometric import sin, cos, sinc
  from sympy.series.series_class import SeriesBase
  from sympy.series.sequences import SeqFormula
  from sympy.sets.sets import Interval
  from sympy.utilities.iterables import is_sequence
label_desc: Use image node_id 1 for calling the FiniteFourierSeries obj's underlying member method code with example usage: obj.__new__(cls, f, limits, exprs) and returns: Expr