code: def _romberg_diff(b, c, k):
      """
      Compute the differences for the Romberg quadrature corrections.
      See Forman Acton's "Real Computing Made Real," p 143.
      """
      tmp = 4.0**k
      return (tmp * c - b) / (tmp - 1.0)
  
imports: from __future__ import annotations
  from typing import TYPE_CHECKING, Callable, Dict, Tuple, Any, cast
  import functools
  import numpy
  import math
  import types
  import warnings
  from numpy import trapz
  from scipy.special import roots_legendre
  from scipy.special import gammaln
label_desc: Use image node_id 16 for calling a global function with example usage: _romberg_diff(b, c, k) and returns: unknown