def _check_antecedents_1(g, x, helper=False):
    """
    Return a condition under which the mellin transform of g exists.
    Any power of x has already been absorbed into the G function,
    so this is just int_0^\infty g dx.

    See [L, section 5.6.1]. (Note that s=1.)

    If ``helper`` is True, only check if the MT exists at infinity, i.e. if
    int_1^\infty g dx exists.
    """
    # NOTE if you update these conditions, please update the documentation as well
    from sympy import Eq, Not, ceiling, Ne, re, unbranched_argument as arg
    delta = g.delta
    eta, _ = _get_coeff_exp(g.argument, x)
    m, n, p, q = S([len(g.bm), len(g.an), len(g.ap), len(g.bq)])
    xi = m + n - p

    if p > q:
        def tr(l):
            return [1 - x for x in l]
        return _check_antecedents_1(meijerg(tr(g.bm), tr(g.bother),
                                            tr(g.an), tr(g.aother), x/eta),
                                    x)

    tmp = []
    for b in g.bm:
        tmp += [-re(b) < 1]
    for a in g.an:
        tmp += [1 < 1 - re(a)]
    cond_3 = And(*tmp)

    for b in g.bother:
        tmp += [-re(b) < 1]
    for a in g.aother:
        tmp += [1 < 1 - re(a)]
    cond_3_star = And(*tmp)

    cond_4 = (-re(g.nu) + (q + 1 - p)/2 > q - p)

    def debug(*msg):
        _debug(*msg)

    debug('Checking antecedents for 1 function:')
    debug('  delta=%s, eta=%s, m=%s, n=%s, p=%s, q=%s'
          % (delta, eta, m, n, p, q))
    debug('  ap = %s, %s' % (list(g.an), list(g.aother)))
    debug('  bq = %s, %s' % (list(g.bm), list(g.bother)))
    debug('  cond_3=%s, cond_3*=%s, cond_4=%s' % (cond_3, cond_3_star, cond_4))

    conds = []

    # case 1
    case1 = []
    tmp1 = [1 <= n, p < q, 1 <= m]
    tmp2 = [1 <= p, 1 <= m, Eq(q, p + 1), Not(And(Eq(n, 0), Eq(m, p + 1)))]
    tmp3 = [1 <= p, Eq(q, p)]
    for k in range(ceiling(delta/2) + 1):
        tmp3 += [Ne(abs(arg(eta)), (delta - 2*k)*pi)]
    tmp = [delta > 0, abs(arg(eta)) < delta*pi]
    extra = [Ne(eta, 0), cond_3]
    if helper:
        extra = []
    for t in [tmp1, tmp2, tmp3]:
        case1 += [And(*(t + tmp + extra))]
    conds += case1
    debug('  case 1:', case1)

    # case 2
    extra = [cond_3]
    if helper:
        extra = []
    case2 = [And(Eq(n, 0), p + 1 <= m, m <= q,
                 abs(arg(eta)) < delta*pi, *extra)]
    conds += case2
    debug('  case 2:', case2)

    # case 3
    extra = [cond_3, cond_4]
    if helper:
        extra = []
    case3 = [And(p < q, 1 <= m, delta > 0, Eq(abs(arg(eta)), delta*pi),
                 *extra)]
    case3 += [And(p <= q - 2, Eq(delta, 0), Eq(abs(arg(eta)), 0), *extra)]
    conds += case3
    debug('  case 3:', case3)

    # TODO altered cases 4-7

    # extra case from wofram functions site:
    # (reproduced verbatim from Prudnikov, section 2.24.2)
    # http://functions.wolfram.com/HypergeometricFunctions/MeijerG/21/02/01/
    case_extra = []
    case_extra += [Eq(p, q), Eq(delta, 0), Eq(arg(eta), 0), Ne(eta, 0)]
    if not helper:
        case_extra += [cond_3]
    s = []
    for a, b in zip(g.ap, g.bq):
        s += [b - a]
    case_extra += [re(Add(*s)) < 0]
    case_extra = And(*case_extra)
    conds += [case_extra]
    debug('  extra case:', [case_extra])

    case_extra_2 = [And(delta > 0, abs(arg(eta)) < delta*pi)]
    if not helper:
        case_extra_2 += [cond_3]
    case_extra_2 = And(*case_extra_2)
    conds += [case_extra_2]
    debug('  second extra case:', [case_extra_2])

    # TODO This leaves only one case from the three listed by Prudnikov.
    #      Investigate if these indeed cover everything; if so, remove the rest.

    return Or(*conds)
dataset/ETHPy150Open sympy/sympy/sympy/integrals/meijerint.py/_check_antecedents_1/original