class_docstr: Cauchy Distribution
  ----
  This class contains methods relating to the Cauchy distribution for time series.
docstr: GASX Cauchy Model Recursion - gradient only
  
  Returns
  ----------
  - Recursion function for GASX Cauchy model - gradient only
docstr_tok: ["GASX","Cauchy","Model","Recursion","-","gradient","only","Returns","--","--","--","--","--","-","Recursion","function","for","GASX","Cauchy","model","-","gradient","only"]
code: def gradientx_recursion():
      """GASX Cauchy Model Recursion - gradient only
  
      Returns
      ----------
      - Recursion function for GASX Cauchy model - gradient only
      """
      return gasx_recursion_cauchy_orderone
  
imports: import numpy
  import scipy.stats
  import scipy.special
  from .family import Family
  from .flat import Flat
  from .normal import Normal
  from .gas_recursions import gas_recursion_cauchy_orderone, gas_recursion_cauchy_ordertwo
  from .gas_recursions import gasx_recursion_cauchy_orderone, gasx_recursion_cauchy_ordertwo
  from .gas_recursions import gas_llev_recursion_cauchy_orderone, gas_llev_recursion_cauchy_ordertwo
  from .gas_recursions import gas_llt_recursion_cauchy_orderone, gas_llt_recursion_cauchy_ordertwo
  from .gas_recursions import gas_reg_recursion_cauchy_orderone, gas_reg_recursion_cauchy_ordertwo
label_desc: Use image node_id 17 for calling the Cauchy obj's underlying member method code with example usage: obj.gradientx_recursion() and returns: gasx_recursion_cauchy_orderone