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    Horn Function

    Horn function (common versions)

    HornH5(a, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(m - n) (z_1^m z_2^n))/((c)_m m! n!) HornH10(a, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(2 m - n) (z_1^m z_2^n))/((c)_m m! n!) HornH8(a, b, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(2 m - n) ((b)_(n - m) z_1^m z_2^n))/(m! n!) HornH6(a, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(2 m + n) (z_1^m z_2^n))/((c)_(m + n) m! n!) HornGamma2(a_1, a_2, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a_1)_(n - m) ((a_2)_(m - n) z_1^m z_2^n))/(m! n!) HornG3(a_1, a_2, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a_1)_(2 n - m) ((a_2)_(2 m - n) z_1^m z_2^n))/(m! n!) HornPhi3(b_1, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((b_1)_m (z_1^m z_2^n))/((c)_(m + n) m! n!) for abs(z_1)<1 HornH30(a, b, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(m - n) ((b)_m z_1^m z_2^n))/((c)_m m! n!) HornH4(a, γ, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(m - n) ((γ)_n z_1^m z_2^n))/((c)_m m! n!) HornH9(a, b, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(2 m - n) ((b)_n z_1^m z_2^n))/((c)_m m! n!) HornH6(a, b, γ, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(2 m - n) ((b)_(n - m) (γ)_n z_1^m z_2^n))/(m! n!) HornH7(a, c, d, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(2 m + n) (z_1^m z_2^n))/((c)_m (d)_n m! n!) HornH3(a, b, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(2 m + n) ((b)_n z_1^m z_2^n))/((c)_(m + n) m! n!) HornH5(a, b, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(2 m + n) ((b)_(n - m) z_1^m z_2^n))/((c)_n m! n!) HornGamma1(a, a_1, a_2, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_m ((a_1)_(n - m) (a_2)_(m - n) z_1^m z_2^n))/(m! n!) HornG1(a, b_1, b_2, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(m + n) ((b_1)_(n - m) (b_2)_(m - n) z_1^m z_2^n))/(m! n!) HornPhi1(a, b, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(m + n) ((b)_m z_1^m z_2^n))/((c)_(m + n) m! n!) for abs(z_1)<1 HornXi2(a, b, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_m ((b)_m z_1^m z_2^n))/((c)_(m + n) m! n!) for abs(z_1)<1 HornPsi2(a, c_1, c_2, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(m + n) (z_1^m z_2^n))/((c_1)_m (c_2)_n m! n!) HornPhi2(b_1, b_2, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((b_1)_m ((b_2)_n z_1^m z_2^n))/((c)_(m + n) m! n!) for abs(z_1)<1 HornH11(a, b, γ, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(m - n) ((b)_n (γ)_n z_1^m z_2^n))/((c)_m m! n!) HornH2(a, b, γ, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(m - n) ((b)_m (γ)_n z_1^m z_2^n))/((c)_m m! n!) HornH1(a, b, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(m - n) ((b)_(m + n) (γ)_n z_1^m z_2^n))/((c)_m m! n!) HornH1(a, b, γ, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(m - n) ((b)_(m + n) (γ)_n z_1^m z_2^n))/((c)_m m! n!) HornH7(a, b, γ, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(2 m - n) ((b)_n (γ)_n z_1^m z_2^n))/((c)_m m! n!) HornH4(a, b, c, d, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(2 m + n) ((b)_n z_1^m z_2^n))/((c)_m (d)_n m! n!) HornG2(a_1, a_2, b_1, b_2, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a_1)_m ((a_2)_n (b_1)_(n - m) (b_2)_(m - n) z_1^m z_2^n))/(m! n!) HornXi1(a_1, a_2, b, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a_1)_m ((a_2)_n (b)_m z_1^m z_2^n))/((c)_(m + n) m! n!) for abs(z_1)<1 HornPsi1(a, b, c_1, c_2, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(m + n) ((b)_m z_1^m z_2^n))/((c_1)_m (c_2)_n m! n!) for abs(z_1)<1 HornH2(a, b, γ, δ, c, z_1, z_2) = sum_(m=0)^∞ sum_(n=0)^∞ ((a)_(m - n) ((b)_m (γ)_n (δ)_n z_1^m z_2^n))/((c)_m m! n!)

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