def rs_sinh(p, x, prec):
    """
    Hyperbolic sine of a series

    Return the series expansion of the sinh of ``p``, about 0.

    Examples
    ========

    >>> from sympy.polys.domains import QQ
    >>> from sympy.polys.rings import ring
    >>> from sympy.polys.ring_series import rs_sinh
    >>> R, x, y = ring('x, y', QQ)
    >>> rs_sinh(x + x*y, x, 4)
    1/6*x**3*y**3 + 1/2*x**3*y**2 + 1/2*x**3*y + 1/6*x**3 + x*y + x

    See Also
    ========

    sinh
    """
    if rs_is_puiseux(p, x):
        return rs_puiseux(rs_sinh, p, x, prec)
    t = rs_exp(p, x, prec)
    t1 = rs_series_inversion(t, x, prec)
    return (t - t1)/2
dataset/ETHPy150Open sympy/sympy/sympy/polys/ring_series.py/rs_sinh/original