code: def eta(lam):
      """Function from DLMF 8.12.1 shifted to be centered at 0."""
      if lam > 0:
          return mp.sqrt(2 * (lam - mp.log(lam + 1)))
      elif lam < 0:
          return -mp.sqrt(2 * (lam - mp.log(lam + 1)))
      else:
          return 0
  
file_path: scipy/scipy/special/_precompute/gammainc_asy.py
imports: import os
  from scipy.special._precompute.utils import lagrange_inversion
label_desc: Use image node_id 3 for calling a global function with example usage: eta(lam) and returns: mp, unknown, int