code: def _frobenius(n, m, p0, q0, p, q, x0, x, c, check=None):
      r"""
      Returns a dict with keys as coefficients and values as their values in terms of C0
      """
      n = int(n)
      # In cases where m1 - m2 is not an integer
      m2 = check
  
      d = Dummy("d")
      numsyms = numbered_symbols("C", start=0)
      numsyms = [next(numsyms) for i in range(n + 1)]
      serlist = []
      for ser in [p, q]:
          # Order term not present
          if ser.is_polynomial(x) and Poly(ser, x).degree() <= n:
              if x0:
                  ser = ser.subs(x, x + x0)
              dict_ = Poly(ser, x).as_dict()
          # Order term present
          else:
              tseries = series(ser, x=x0, n=n + 1)
              # Removing order
              dict_ = Poly(
                  list(ordered(tseries.args))[:-1], x
              ).as_dict()
          # Fill in with zeros, if coefficients are zero.
          for i in range(n + 1):
              if (i,) not in dict_:
                  dict_[(i,)] = S.Zero
          serlist.append(dict_)
  
      pseries = serlist[0]
      qseries = serlist[1]
      indicial = d * (d - 1) + d * p0 + q0
      frobdict = {}
      for i in range(1, n + 1):
          num = c * (m * pseries[(i,)] + qseries[(i,)])
          for j in range(1, i):
              sym = Symbol("C" + str(j))
              num += frobdict[sym] * (
                  (m + j) * pseries[(i - j,)] + qseries[(i - j,)]
              )
  
          # Checking for cases when m1 - m2 is an integer. If num equals zero
          # then a second Frobenius series solution cannot be found. If num is not zero
          # then set constant as zero and proceed.
          if m2 is not None and i == m2 - m:
              if num:
                  return False
              else:
                  frobdict[numsyms[i]] = S.Zero
          else:
              frobdict[numsyms[i]] = -num / (indicial.subs(d, m + i))
  
      return frobdict
  
imports: from sympy.core import Add, S, Mul, Pow, oo
  from sympy.core.containers import Tuple
  from sympy.core.expr import AtomicExpr, Expr
  from sympy.core.function import Function, Derivative, AppliedUndef, diff, expand, expand_mul, Subs
  from sympy.core.multidimensional import vectorize
  from sympy.core.numbers import nan, zoo, Number
  from sympy.core.relational import Equality, Eq
  from sympy.core.sorting import default_sort_key, ordered
  from sympy.core.symbol import Symbol, Wild, Dummy, symbols
  from sympy.core.sympify import sympify
  from sympy.core.traversal import preorder_traversal
  from sympy.logic.boolalg import BooleanAtom, BooleanTrue, BooleanFalse
  from sympy.functions import exp, log, sqrt
  from sympy.functions.combinatorial.factorials import factorial
  from sympy.integrals.integrals import Integral
  from sympy.polys import Poly, terms_gcd, PolynomialError, lcm
  from sympy.polys.polytools import cancel
  from sympy.series import Order
  from sympy.series.series import series
  from sympy.simplify import collect, logcombine, powsimp, separatevars, simplify, cse
  from sympy.simplify.radsimp import collect_const
  from sympy.solvers import checksol, solve
  from sympy.utilities import numbered_symbols
  from sympy.utilities.iterables import uniq, sift, iterable
  from sympy.solvers.deutils import _preprocess, ode_order, _desolve
  from .single import SingleODEProblem, SingleODESolver, solver_map
label_desc: Use image node_id 24 for calling a global function with example usage: _frobenius(n, m, p0, q0, p, q, x0, x, c, check) and returns: frobdict, False