code: def rs_asin(p, x, prec):
      """
      Arcsine of a series
  
      Return the series expansion of the asin of ``p``, about 0.
  
      Examples
      ========
  
      >>> from sympy.polys.domains import QQ
      >>> from sympy.polys.rings import ring
      >>> from sympy.polys.ring_series import rs_asin
      >>> R, x, y = ring('x, y', QQ)
      >>> rs_asin(x, x, 8)
      5/112*x**7 + 3/40*x**5 + 1/6*x**3 + x
  
      See Also
      ========
  
      asin
      """
      if rs_is_puiseux(p, x):
          return rs_puiseux(rs_asin, p, x, prec)
      if _has_constant_term(p, x):
          raise NotImplementedError(
              "Polynomial must not have constant term in "
              "series variables"
          )
      R = p.ring
      if x in R.gens:
          # get a good value
          if len(p) > 20:
              dp = rs_diff(p, x)
              p1 = 1 - rs_square(p, x, prec - 1)
              p1 = rs_nth_root(p1, -2, x, prec - 1)
              p1 = rs_mul(dp, p1, x, prec - 1)
              return rs_integrate(p1, x)
          one = R(1)
          c = [0, one, 0]
          for k in range(3, prec, 2):
              c.append((k - 2) ** 2 * c[-2] / (k * (k - 1)))
              c.append(0)
          return rs_series_from_list(p, c, x, prec)
  
      else:
          raise NotImplementedError
  
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 32 for calling a global function with example usage: rs_asin(p, x, prec) and returns: rs_puiseux, rs_series_from_list, rs_integrate