code: def rs_cosh(p, x, prec):
      """
      Hyperbolic cosine of a series
  
      Return the series expansion of the cosh of ``p``, about 0.
  
      Examples
      ========
  
      >>> from sympy.polys.domains import QQ
      >>> from sympy.polys.rings import ring
      >>> from sympy.polys.ring_series import rs_cosh
      >>> R, x, y = ring('x, y', QQ)
      >>> rs_cosh(x + x*y, x, 4)
      1/2*x**2*y**2 + x**2*y + 1/2*x**2 + 1
  
      See Also
      ========
  
      cosh
      """
      if rs_is_puiseux(p, x):
          return rs_puiseux(rs_cosh, p, x, prec)
      t = rs_exp(p, x, prec)
      t1 = rs_series_inversion(t, x, prec)
      return (t + t1) / 2
  
imports: from sympy.polys.domains import QQ, EX
  from sympy.polys.rings import PolyElement, ring, sring
  from sympy.polys.polyerrors import DomainError
  from sympy.polys.monomials import monomial_min, monomial_mul, monomial_div, monomial_ldiv
  from mpmath.libmp.libintmath import ifac
  from sympy.core import PoleError, Function, Expr
  from sympy.core.numbers import Rational
  from sympy.core.intfunc import igcd
  from sympy.functions import sin, cos, tan, atan, exp, atanh, tanh, log, ceiling
  from sympy.utilities.misc import as_int
  from mpmath.libmp.libintmath import giant_steps
  import math
label_desc: Use image node_id 42 for calling a global function with example usage: rs_cosh(p, x, prec) and returns: unknown, rs_puiseux