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    Lauricella Functions

    Lauricella function (common versions)

    LauricellaFA(a, {b_1, ..., b_n}, {c_1, ..., c_n}, {z_1, ..., z_n}) = sum_(k_1=0)^∞ ... sum_(k_n=0)^∞ (( product_(j=1)^n z_j^(k_j)/(k_j !)) ((a)_( sum_(j=1)^n k_j) product_(j=1)^n (b_j)_(k_j)))/( product_(j=1)^n (c_j)_(k_j)) for sum_(k=1)^n abs(z_k)<1 LauricellaFB({a_1, ..., a_n}, {b_1, ..., b_n}, c, {z_1, ..., z_n}) = sum_(k_1=0)^∞ ... sum_(k_n=0)^∞ (( product_(j=1)^n z_j^(k_j)/(k_j !)) (( product_(j=1)^n (a_j)_(k_j)) product_(j=1)^n (b_j)_(k_j)))/(c)_( sum_(j=1)^n k_j) for max( left bracketing bar z_1 right bracketing bar , ..., left bracketing bar z_n right bracketing bar )<1 LauricellaFC(a, b, {c_1, ..., c_n}, {z_1, ..., z_n}) = sum_(k_1=0)^∞ ... sum_(k_n=0)^∞ (( product_(j=1)^n z_j^(k_j)/(k_j !)) ((a)_( sum_(j=1)^n k_j) (b)_( sum_(j=1)^n k_j)))/( product_(j=1)^n (c_j)_(k_j)) for sum_(k=1)^n sqrt(abs(z_k))<1

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