code: def finite_check(f, x, L):
      def check_fx(exprs, x):
          return x not in exprs.free_symbols
  
      def check_sincos(_expr, x, L):
          if isinstance(_expr, (sin, cos)):
              sincos_args = _expr.args[0]
  
              if sincos_args.match(a * (pi / L) * x + b) is not None:
                  return True
              else:
                  return False
  
      from sympy.simplify.fu import TR2, TR1, sincos_to_sum
  
      _expr = sincos_to_sum(TR2(TR1(f)))
      add_coeff = _expr.as_coeff_add()
  
      a = Wild(
          "a",
          properties=[
              lambda k: k.is_Integer,
              lambda k: k != S.Zero,
          ],
      )
      b = Wild(
          "b",
          properties=[
              lambda k: x not in k.free_symbols,
          ],
      )
  
      for s in add_coeff[1]:
          mul_coeffs = s.as_coeff_mul()[1]
          for t in mul_coeffs:
              if not (check_fx(t, x) or check_sincos(t, x, L)):
                  return False, f
  
      return True, _expr
  
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 4 for calling a global function with example usage: finite_check(f, x, L) and returns: True,  _expr, unknown, True, False, False,  f