def _create_lookup_table(table):
    def wild(n):
        return Wild(n, exclude=[z])
    p, q, a, b, c = list(map(wild, 'pqabc'))
    n = Wild('n', properties=[lambda x: x.is_Integer and x > 0])
    t = p*z**q

    def add(formula, an, ap, bm, bq, arg=t, fac=S(1), cond=True, hint=True):
        table.setdefault(_mytype(formula, z), []).append((formula,
                                     [(fac, meijerg(an, ap, bm, bq, arg))], cond, hint))

    def addi(formula, inst, cond, hint=True):
        table.setdefault(
            _mytype(formula, z), []).append((formula, inst, cond, hint))

    def constant(a):
        return [(a, meijerg([1], [], [], [0], z)),
                (a, meijerg([], [1], [0], [], z))]
    table[()] = [(a, constant(a), True, True)]

    # [P], Section 8.

    from sympy import unpolarify, Function, Not

    class IsNonPositiveInteger(Function):

        @classmethod
        def eval(cls, arg):
            arg = unpolarify(arg)
            if arg.is_Integer is True:
                return arg <= 0

    # Section 8.4.2
    from sympy import (gamma, pi, cos, exp, re, sin, sinc, sqrt, sinh, cosh,
                       factorial, log, erf, erfc, erfi, polar_lift)
    # TODO this needs more polar_lift (c/f entry for exp)
    add(Heaviside(t - b)*(t - b)**(a - 1), [a], [], [], [0], t/b,
        gamma(a)*b**(a - 1), And(b > 0))
    add(Heaviside(b - t)*(b - t)**(a - 1), [], [a], [0], [], t/b,
        gamma(a)*b**(a - 1), And(b > 0))
    add(Heaviside(z - (b/p)**(1/q))*(t - b)**(a - 1), [a], [], [], [0], t/b,
        gamma(a)*b**(a - 1), And(b > 0))
    add(Heaviside((b/p)**(1/q) - z)*(b - t)**(a - 1), [], [a], [0], [], t/b,
        gamma(a)*b**(a - 1), And(b > 0))
    add((b + t)**(-a), [1 - a], [], [0], [], t/b, b**(-a)/gamma(a),
        hint=Not(IsNonPositiveInteger(a)))
    add(abs(b - t)**(-a), [1 - a], [(1 - a)/2], [0], [(1 - a)/2], t/b,
        pi/(gamma(a)*cos(pi*a/2))*abs(b)**(-a), re(a) < 1)
    add((t**a - b**a)/(t - b), [0, a], [], [0, a], [], t/b,
        b**(a - 1)*sin(a*pi)/pi)

    # 12
    def A1(r, sign, nu):
        return pi**(-S(1)/2)*(-sign*nu/2)**(1 - 2*r)

    def tmpadd(r, sgn):
        # XXX the a**2 is bad for matching
        add((sqrt(a**2 + t) + sgn*a)**b/(a**2 + t)**r,
            [(1 + b)/2, 1 - 2*r + b/2], [],
            [(b - sgn*b)/2], [(b + sgn*b)/2], t/a**2,
            a**(b - 2*r)*A1(r, sgn, b))
    tmpadd(0, 1)
    tmpadd(0, -1)
    tmpadd(S(1)/2, 1)
    tmpadd(S(1)/2, -1)

    # 13
    def tmpadd(r, sgn):
        add((sqrt(a + p*z**q) + sgn*sqrt(p)*z**(q/2))**b/(a + p*z**q)**r,
            [1 - r + sgn*b/2], [1 - r - sgn*b/2], [0, S(1)/2], [],
            p*z**q/a, a**(b/2 - r)*A1(r, sgn, b))
    tmpadd(0, 1)
    tmpadd(0, -1)
    tmpadd(S(1)/2, 1)
    tmpadd(S(1)/2, -1)
    # (those after look obscure)

    # Section 8.4.3
    add(exp(polar_lift(-1)*t), [], [], [0], [])

    # TODO can do sin^n, sinh^n by expansion ... where?
    # 8.4.4 (hyperbolic functions)
    add(sinh(t), [], [1], [S(1)/2], [1, 0], t**2/4, pi**(S(3)/2))
    add(cosh(t), [], [S(1)/2], [0], [S(1)/2, S(1)/2], t**2/4, pi**(S(3)/2))

    # Section 8.4.5
    # TODO can do t + a. but can also do by expansion... (XXX not really)
    add(sin(t), [], [], [S(1)/2], [0], t**2/4, sqrt(pi))
    add(cos(t), [], [], [0], [S(1)/2], t**2/4, sqrt(pi))

    # Section 8.4.6 (sinc function)
    add(sinc(t), [], [], [0], [S(-1)/2], t**2/4, sqrt(pi)/2)

    # Section 8.5.5
    def make_log1(subs):
        N = subs[n]
        return [((-1)**N*factorial(N),
                 meijerg([], [1]*(N + 1), [0]*(N + 1), [], t))]

    def make_log2(subs):
        N = subs[n]
        return [(factorial(N),
                 meijerg([1]*(N + 1), [], [], [0]*(N + 1), t))]
    # TODO these only hold for positive p, and can be made more general
    #      but who uses log(x)*Heaviside(a-x) anyway ...
    # TODO also it would be nice to derive them recursively ...
    addi(log(t)**n*Heaviside(1 - t), make_log1, True)
    addi(log(t)**n*Heaviside(t - 1), make_log2, True)

    def make_log3(subs):
        return make_log1(subs) + make_log2(subs)
    addi(log(t)**n, make_log3, True)
    addi(log(t + a),
         constant(log(a)) + [(S(1), meijerg([1, 1], [], [1], [0], t/a))],
         True)
    addi(log(abs(t - a)), constant(log(abs(a))) +
         [(pi, meijerg([1, 1], [S(1)/2], [1], [0, S(1)/2], t/a))],
         True)
    # TODO log(x)/(x+a) and log(x)/(x-1) can also be done. should they
    #      be derivable?
    # TODO further formulae in this section seem obscure

    # Sections 8.4.9-10
    # TODO

    # Section 8.4.11
    from sympy import Ei, I, expint, Si, Ci, Shi, Chi, fresnels, fresnelc
    addi(Ei(t),
         constant(-I*pi) + [(S(-1), meijerg([], [1], [0, 0], [],
                  t*polar_lift(-1)))],
         True)

    # Section 8.4.12
    add(Si(t), [1], [], [S(1)/2], [0, 0], t**2/4, sqrt(pi)/2)
    add(Ci(t), [], [1], [0, 0], [S(1)/2], t**2/4, -sqrt(pi)/2)

    # Section 8.4.13
    add(Shi(t), [S(1)/2], [], [0], [S(-1)/2, S(-1)/2], polar_lift(-1)*t**2/4,
        t*sqrt(pi)/4)
    add(Chi(t), [], [S(1)/2, 1], [0, 0], [S(1)/2, S(1)/2], t**2/4, -
        pi**S('3/2')/2)

    # generalized exponential integral
    add(expint(a, t), [], [a], [a - 1, 0], [], t)

    # Section 8.4.14
    add(erf(t), [1], [], [S(1)/2], [0], t**2, 1/sqrt(pi))
    # TODO exp(-x)*erf(I*x) does not work
    add(erfc(t), [], [1], [0, S(1)/2], [], t**2, 1/sqrt(pi))
    # This formula for erfi(z) yields a wrong(?) minus sign
    #add(erfi(t), [1], [], [S(1)/2], [0], -t**2, I/sqrt(pi))
    add(erfi(t), [S(1)/2], [], [0], [-S(1)/2], -t**2, t/sqrt(pi))

    # Fresnel Integrals
    add(fresnels(t), [1], [], [S(3)/4], [0, S(1)/4], pi**2*t**4/16, S(1)/2)
    add(fresnelc(t), [1], [], [S(1)/4], [0, S(3)/4], pi**2*t**4/16, S(1)/2)

    ##### bessel-type functions #####
    from sympy import besselj, bessely, besseli, besselk

    # Section 8.4.19
    add(besselj(a, t), [], [], [a/2], [-a/2], t**2/4)

    # all of the following are derivable
    #add(sin(t)*besselj(a, t), [S(1)/4, S(3)/4], [], [(1+a)/2],
    #    [-a/2, a/2, (1-a)/2], t**2, 1/sqrt(2))
    #add(cos(t)*besselj(a, t), [S(1)/4, S(3)/4], [], [a/2],
    #    [-a/2, (1+a)/2, (1-a)/2], t**2, 1/sqrt(2))
    #add(besselj(a, t)**2, [S(1)/2], [], [a], [-a, 0], t**2, 1/sqrt(pi))
    #add(besselj(a, t)*besselj(b, t), [0, S(1)/2], [], [(a + b)/2],
    #    [-(a+b)/2, (a - b)/2, (b - a)/2], t**2, 1/sqrt(pi))

    # Section 8.4.20
    add(bessely(a, t), [], [-(a + 1)/2], [a/2, -a/2], [-(a + 1)/2], t**2/4)

    # TODO all of the following should be derivable
    #add(sin(t)*bessely(a, t), [S(1)/4, S(3)/4], [(1 - a - 1)/2],
    #    [(1 + a)/2, (1 - a)/2], [(1 - a - 1)/2, (1 - 1 - a)/2, (1 - 1 + a)/2],
    #    t**2, 1/sqrt(2))
    #add(cos(t)*bessely(a, t), [S(1)/4, S(3)/4], [(0 - a - 1)/2],
    #    [(0 + a)/2, (0 - a)/2], [(0 - a - 1)/2, (1 - 0 - a)/2, (1 - 0 + a)/2],
    #    t**2, 1/sqrt(2))
    #add(besselj(a, t)*bessely(b, t), [0, S(1)/2], [(a - b - 1)/2],
    #    [(a + b)/2, (a - b)/2], [(a - b - 1)/2, -(a + b)/2, (b - a)/2],
    #    t**2, 1/sqrt(pi))
    #addi(bessely(a, t)**2,
    #     [(2/sqrt(pi), meijerg([], [S(1)/2, S(1)/2 - a], [0, a, -a],
    #                           [S(1)/2 - a], t**2)),
    #      (1/sqrt(pi), meijerg([S(1)/2], [], [a], [-a, 0], t**2))],
    #     True)
    #addi(bessely(a, t)*bessely(b, t),
    #     [(2/sqrt(pi), meijerg([], [0, S(1)/2, (1 - a - b)/2],
    #                           [(a + b)/2, (a - b)/2, (b - a)/2, -(a + b)/2],
    #                           [(1 - a - b)/2], t**2)),
    #      (1/sqrt(pi), meijerg([0, S(1)/2], [], [(a + b)/2],
    #                           [-(a + b)/2, (a - b)/2, (b - a)/2], t**2))],
    #     True)

    # Section 8.4.21 ?
    # Section 8.4.22
    add(besseli(a, t), [], [(1 + a)/2], [a/2], [-a/2, (1 + a)/2], t**2/4, pi)
    # TODO many more formulas. should all be derivable

    # Section 8.4.23
    add(besselk(a, t), [], [], [a/2, -a/2], [], t**2/4, S(1)/2)
    # TODO many more formulas. should all be derivable

    # Complete elliptic integrals K(z) and E(z)
    from sympy import elliptic_k, elliptic_e
    add(elliptic_k(t), [S.Half, S.Half], [], [0], [0], -t, S.Half)
    add(elliptic_e(t), [S.Half, 3*S.Half], [], [0], [0], -t, -S.Half/2)


####################################################################
# First some helper functions.
####################################################################
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