code: def construct_c_case_2(num, den, x, pole, mul):
      # Generate the coefficients using the recurrence
      # relation mentioned in (5.14) in the thesis (Pg 80)
  
      # r_i = mul/2
      ri = mul // 2
  
      # Find the Laurent series coefficients about the pole
      ser = rational_laurent_series(num, den, x, pole, mul, 6)
  
      # Start with an empty memo to store the coefficients
      # This is for the plus case
      cplus = [0 for i in range(ri)]
  
      # Base Case
      cplus[ri - 1] = sqrt(ser[2 * ri])
  
      # Iterate backwards to find all coefficients
      s = ri - 1
      sm = 0
      for s in range(ri - 1, 0, -1):
          sm = 0
          for j in range(s + 1, ri):
              sm += cplus[j - 1] * cplus[ri + s - j - 1]
          if s != 1:
              cplus[s - 1] = (ser[ri + s] - sm) / (2 * cplus[ri - 1])
  
      # Memo for the minus case
      cminus = [-x for x in cplus]
  
      # Find the 0th coefficient in the recurrence
      cplus[0] = (ser[ri + s] - sm - ri * cplus[ri - 1]) / (
          2 * cplus[ri - 1]
      )
      cminus[0] = (ser[ri + s] - sm - ri * cminus[ri - 1]) / (
          2 * cminus[ri - 1]
      )
  
      # Add both the plus and minus cases' coefficients
      if cplus != cminus:
          return [cplus, cminus]
      return cplus
  
imports: from itertools import product
  from sympy.core import S
  from sympy.core.add import Add
  from sympy.core.numbers import oo, Float
  from sympy.core.function import count_ops
  from sympy.core.relational import Eq
  from sympy.core.symbol import symbols, Symbol, Dummy
  from sympy.functions import sqrt, exp
  from sympy.functions.elementary.complexes import sign
  from sympy.integrals.integrals import Integral
  from sympy.polys.domains import ZZ
  from sympy.polys.polytools import Poly
  from sympy.polys.polyroots import roots
  from sympy.solvers.solveset import linsolve
label_desc: Use image node_id 11 for calling a global function with example usage: construct_c_case_2(num, den, x, pole, mul) and returns: cplus, list