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    Generalized Hypergeometric Differential Equation

    Generalized hypergeometric differential equation

    z^q w^(q + 1)(z) + z^(q - 1) (1/2 q (q - 1) + sum_(k=1)^q b_k) w^(q)(z) - z^p w^(p)(z) - z^(p - 1) (1/2 p (p - 1) + sum_(l=1)^p a_l) w^(p - 1)(z) + (d/(dz) Fold[{f, k} function z (df)/(dz) + (b_k - 1) f, w(z), {1, ..., q}] - Fold[{f, l} function z (df)/(dz) + a_l f, w(z), {1, ..., p}] - z^q w^(q + 1)(z) - z^(q - 1) (1/2 q (q - 1) + sum_(k=1)^q b_k) w^(q)(z) + z^p w^(p)(z) + z^(p - 1) (1/2 p (p - 1) + sum_(k=1)^p a_k) w^(p - 1)(z) + w(z) product_(l=1)^p a_l) - w(z) product_(l=1)^p a_l = 0 for w(z) = c_1 _3 F^~_3(a_1, ..., a_p;b_1, ..., b_q;z) + c_2 sum_(k=1)^q G_(3, 8)^(2, 3) (z|1 - a_1, ..., 1 - a_p 0, 1 - b_k, 1 - b_1, ..., 1 - b_(k - 1), 1 - b_(k + 1), ..., 1 - b_q) + ... + c_q sum_(k=1)^q G_(3, 8)^(7, 3) ((-1)^q z|1 - a_1, ..., 1 - a_p 0, 1 - b_1, ..., 1 - b_(k - 1), 1 - b_(k + 1), ..., 1 - b_q, 1 - b_k) + c_(q + 1) G_(3, 4)^(4, 3) ((-1)^(q + 1) z|1 - a_1, ..., 1 - a_p 0, 1 - b_1, ..., 1 - b_q)

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