html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cosh

 http://functions.wolfram.com/01.20.21.4936.01

 Input Form

 Integrate[z^n E^(b z^2 + d z + e) Cos[a z^2 + p z + q]^m Sinh[w z^2 + s z + t]^u Cosh[c z^2 + f z + g]^v, z] == (-I^u) 2^(-1 - m - u - v) b^(-1 - n) E^(-(d^2/(4 b)) + e) Binomial[m, m/2] Binomial[u, u/2] Binomial[v, v/2] (1 - Mod[m, 2]) (1 - Mod[u, 2]) (1 - Mod[v, 2]) Sum[2^(l - n) (-d)^(-l + n) (d + 2 b z)^(1 + l) (-((d + 2 b z)^2/b))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + 2 b z)^2/(4 b))], {l, 0, n}] - I^u 2^(-1 - m - u - v) Binomial[u, u/2] Binomial[v, v/2] (1 - Mod[u, 2]) (1 - Mod[v, 2]) Sum[Binomial[m, j] (E^(e - (d + I (2 j - m) p)^2/(4 (b + I a (2 j - m))) + I (2 j - m) q) (b + I a (2 j - m))^(-1 - n) Sum[2^(l - n) (-d - I (2 j - m) p)^ (-l + n) (d + I (2 j - m) p + 2 (b + I a (2 j - m)) z)^(1 + l) (-((d + I (2 j - m) p + 2 (b + I a (2 j - m)) z)^2/ (b + I a (2 j - m))))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + I (2 j - m) p + 2 (b + I a (2 j - m)) z)^2/ (4 (b + I a (2 j - m))))], {l, 0, n}] + E^(e - (d + I (-2 j + m) p)^2/(4 (b + I a (-2 j + m))) + I (-2 j + m) q) (b + I a (-2 j + m))^(-1 - n) Sum[2^(l - n) (-d - I (-2 j + m) p)^(-l + n) (d + I (-2 j + m) p + 2 (b + I a (-2 j + m)) z)^(1 + l) (-((d + I (-2 j + m) p + 2 (b + I a (-2 j + m)) z)^2/ (b + I a (-2 j + m))))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + I (-2 j + m) p + 2 (b + I a (-2 j + m)) z)^ 2/(4 (b + I a (-2 j + m))))], {l, 0, n}]), {j, 0, Floor[(1/2) (-1 + m)]}] - I^u 2^(-1 - m - u - v) Binomial[m, m/2] Binomial[u, u/2] (1 - Mod[m, 2]) (1 - Mod[u, 2]) Sum[Binomial[v, j] (E^(e - (d + f (2 j - v))^2/(4 (b + c (2 j - v))) + g (2 j - v)) (b + c (2 j - v))^(-1 - n) Sum[2^(l - n) (-d - f (2 j - v))^(-l + n) (d + f (2 j - v) + 2 (b + c (2 j - v)) z)^(1 + l) (-((d + f (2 j - v) + 2 (b + c (2 j - v)) z)^2/(b + c (2 j - v))))^ ((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + f (2 j - v) + 2 (b + c (2 j - v)) z)^2/ (4 (b + c (2 j - v))))], {l, 0, n}] + E^(e + g (-2 j + v) - (d + f (-2 j + v))^2/(4 (b + c (-2 j + v)))) (b + c (-2 j + v))^(-1 - n) Sum[2^(l - n) (-d - f (-2 j + v))^ (-l + n) (d + f (-2 j + v) + 2 (b + c (-2 j + v)) z)^(1 + l) (-((d + f (-2 j + v) + 2 (b + c (-2 j + v)) z)^2/ (b + c (-2 j + v))))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + f (-2 j + v) + 2 (b + c (-2 j + v)) z)^2/ (4 (b + c (-2 j + v))))], {l, 0, n}]), {j, 0, Floor[(1/2) (-1 + v)]}] - I^u 2^(-1 - m - u - v) Binomial[m, m/2] Binomial[v, v/2] (1 - Mod[m, 2]) (1 - Mod[v, 2]) Sum[(-1)^i Binomial[u, i] (E^(e + t (2 i - u) + (I Pi u)/2 - (d + s (2 i - u))^2/ (4 (b + (2 i - u) w))) (b + (2 i - u) w)^(-1 - n) Sum[2^(l - n) (-d - s (2 i - u))^(-l + n) (d + s (2 i - u) + 2 (b + (2 i - u) w) z)^(1 + l) (-((d + s (2 i - u) + 2 (b + (2 i - u) w) z)^2/(b + (2 i - u) w)))^ ((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + s (2 i - u) + 2 (b + (2 i - u) w) z)^2/ (4 (b + (2 i - u) w)))], {l, 0, n}] + E^(e - (I Pi u)/2 + t (-2 i + u) - (d + s (-2 i + u))^2/ (4 (b + (-2 i + u) w))) (b + (-2 i + u) w)^(-1 - n) Sum[2^(l - n) (-d - s (-2 i + u))^(-l + n) (d + s (-2 i + u) + 2 (b + (-2 i + u) w) z)^(1 + l) (-((d + s (-2 i + u) + 2 (b + (-2 i + u) w) z)^2/ (b + (-2 i + u) w)))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + s (-2 i + u) + 2 (b + (-2 i + u) w) z)^2/ (4 (b + (-2 i + u) w)))], {l, 0, n}]), {i, 0, Floor[(1/2) (-1 + u)]}] - I^u 2^(-1 - m - u - v) Binomial[u, u/2] (1 - Mod[u, 2]) Sum[Binomial[m, k] Sum[Binomial[v, j] (E^(e + I (2 k - m) q - (d + I (2 k - m) p + f (2 j - v))^2/(4 (b + I a (2 k - m) + c (2 j - v))) + g (2 j - v)) (b + I a (2 k - m) + c (2 j - v))^ (-1 - n) Sum[2^(l - n) (-d - I (2 k - m) p - f (2 j - v))^(-l + n) (d + I (2 k - m) p + f (2 j - v) + 2 (b + I a (2 k - m) + c (2 j - v)) z)^(1 + l) (-((d + I (2 k - m) p + f (2 j - v) + 2 (b + I a (2 k - m) + c (2 j - v)) z)^2/(b + I a (2 k - m) + c (2 j - v))))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + I (2 k - m) p + f (2 j - v) + 2 (b + I a (2 k - m) + c (2 j - v)) z)^2/(4 (b + I a (2 k - m) + c (2 j - v))))], {l, 0, n}] + E^(e + I (-2 k + m) q - (d + I (-2 k + m) p + f (2 j - v))^2/ (4 (b + I a (-2 k + m) + c (2 j - v))) + g (2 j - v)) (b + I a (-2 k + m) + c (2 j - v))^(-1 - n) Sum[2^(l - n) (-d - I (-2 k + m) p - f (2 j - v))^(-l + n) (d + I (-2 k + m) p + f (2 j - v) + 2 (b + I a (-2 k + m) + c (2 j - v)) z)^(1 + l) (-((d + I (-2 k + m) p + f (2 j - v) + 2 (b + I a (-2 k + m) + c (2 j - v)) z)^2/(b + I a (-2 k + m) + c (2 j - v))))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + I (-2 k + m) p + f (2 j - v) + 2 (b + I a (-2 k + m) + c (2 j - v)) z)^2/(4 (b + I a (-2 k + m) + c (2 j - v))))], {l, 0, n}] + E^(e + I (2 k - m) q + g (-2 j + v) - (d + I (2 k - m) p + f (-2 j + v))^2/(4 (b + I a (2 k - m) + c (-2 j + v)))) (b + I a (2 k - m) + c (-2 j + v))^(-1 - n) Sum[2^(l - n) (-d - I (2 k - m) p - f (-2 j + v))^(-l + n) (d + I (2 k - m) p + f (-2 j + v) + 2 (b + I a (2 k - m) + c (-2 j + v)) z)^(1 + l) (-((d + I (2 k - m) p + f (-2 j + v) + 2 (b + I a (2 k - m) + c (-2 j + v)) z)^2/( b + I a (2 k - m) + c (-2 j + v))))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + I (2 k - m) p + f (-2 j + v) + 2 (b + I a (2 k - m) + c (-2 j + v)) z)^2/(4 (b + I a (2 k - m) + c (-2 j + v))))], {l, 0, n}] + E^(e + I (-2 k + m) q + g (-2 j + v) - (d + I (-2 k + m) p + f (-2 j + v))^2/(4 (b + I a (-2 k + m) + c (-2 j + v)))) (b + I a (-2 k + m) + c (-2 j + v))^(-1 - n) Sum[2^(l - n) (-d - I (-2 k + m) p - f (-2 j + v))^(-l + n) (d + I (-2 k + m) p + f (-2 j + v) + 2 (b + I a (-2 k + m) + c (-2 j + v)) z)^(1 + l) (-((d + I (-2 k + m) p + f (-2 j + v) + 2 (b + I a (-2 k + m) + c (-2 j + v)) z)^2/( b + I a (-2 k + m) + c (-2 j + v))))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + I (-2 k + m) p + f (-2 j + v) + 2 (b + I a (-2 k + m) + c (-2 j + v)) z)^2/(4 (b + I a (-2 k + m) + c (-2 j + v))))], {l, 0, n}]), {j, 0, Floor[(1/2) (-1 + v)]}], {k, 0, Floor[(1/2) (-1 + m)]}] - I^u 2^(-1 - m - u - v) Binomial[v, v/2] (1 - Mod[v, 2]) Sum[Binomial[m, j] Sum[(-1)^i Binomial[u, i] (E^(e + I (2 j - m) q + t (2 i - u) + (I Pi u)/2 - (d + I (2 j - m) p + s (2 i - u))^2/(4 (b + I a (2 j - m) + (2 i - u) w))) (b + I a (2 j - m) + (2 i - u) w)^(-1 - n) Sum[2^(l - n) (-d - I (2 j - m) p - s (2 i - u))^(-l + n) (d + I (2 j - m) p + s (2 i - u) + 2 (b + I a (2 j - m) + (2 i - u) w) z)^(1 + l) (-((d + I (2 j - m) p + s (2 i - u) + 2 (b + I a (2 j - m) + (2 i - u) w) z)^2/(b + I a (2 j - m) + (2 i - u) w)))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + I (2 j - m) p + s (2 i - u) + 2 (b + I a (2 j - m) + (2 i - u) w) z)^2/(4 (b + I a (2 j - m) + (2 i - u) w)))], {l, 0, n}] + E^(e + I (-2 j + m) q + t (2 i - u) + (I Pi u)/2 - (d + I (-2 j + m) p + s (2 i - u))^2/(4 (b + I a (-2 j + m) + (2 i - u) w))) (b + I a (-2 j + m) + (2 i - u) w)^(-1 - n) Sum[2^(l - n) (-d - I (-2 j + m) p - s (2 i - u))^(-l + n) (d + I (-2 j + m) p + s (2 i - u) + 2 (b + I a (-2 j + m) + (2 i - u) w) z)^(1 + l) (-((d + I (-2 j + m) p + s (2 i - u) + 2 (b + I a (-2 j + m) + (2 i - u) w) z)^2/(b + I a (-2 j + m) + (2 i - u) w)))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + I (-2 j + m) p + s (2 i - u) + 2 (b + I a (-2 j + m) + (2 i - u) w) z)^2/(4 (b + I a (-2 j + m) + (2 i - u) w)))], {l, 0, n}] + E^(e + I (2 j - m) q - (I Pi u)/2 + t (-2 i + u) - (d + I (2 j - m) p + s (-2 i + u))^2/(4 (b + I a (2 j - m) + (-2 i + u) w))) (b + I a (2 j - m) + (-2 i + u) w)^(-1 - n) Sum[2^(l - n) (-d - I (2 j - m) p - s (-2 i + u))^(-l + n) (d + I (2 j - m) p + s (-2 i + u) + 2 (b + I a (2 j - m) + (-2 i + u) w) z)^(1 + l) (-((d + I (2 j - m) p + s (-2 i + u) + 2 (b + I a (2 j - m) + (-2 i + u) w) z)^2/( b + I a (2 j - m) + (-2 i + u) w)))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + I (2 j - m) p + s (-2 i + u) + 2 (b + I a (2 j - m) + (-2 i + u) w) z)^2/(4 (b + I a (2 j - m) + (-2 i + u) w)))], {l, 0, n}] + E^(e + I (-2 j + m) q - (I Pi u)/2 + t (-2 i + u) - (d + I (-2 j + m) p + s (-2 i + u))^2/(4 (b + I a (-2 j + m) + (-2 i + u) w))) (b + I a (-2 j + m) + (-2 i + u) w)^(-1 - n) Sum[2^(l - n) (-d - I (-2 j + m) p - s (-2 i + u))^(-l + n) (d + I (-2 j + m) p + s (-2 i + u) + 2 (b + I a (-2 j + m) + (-2 i + u) w) z)^(1 + l) (-((d + I (-2 j + m) p + s (-2 i + u) + 2 (b + I a (-2 j + m) + (-2 i + u) w) z)^2/( b + I a (-2 j + m) + (-2 i + u) w)))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + I (-2 j + m) p + s (-2 i + u) + 2 (b + I a (-2 j + m) + (-2 i + u) w) z)^2/(4 (b + I a (-2 j + m) + (-2 i + u) w)))], {l, 0, n}]), {i, 0, Floor[(1/2) (-1 + u)]}], {j, 0, Floor[(1/2) (-1 + m)]}] - I^u 2^(-1 - m - u - v) Binomial[m, m/2] (1 - Mod[m, 2]) Sum[Binomial[v, j] Sum[(-1)^i Binomial[u, i] (E^(e + t (2 i - u) + (I Pi u)/2 + g (2 j - v) - (d + s (2 i - u) + f (2 j - v))^2/(4 (b + c (2 j - v) + (2 i - u) w))) (b + c (2 j - v) + (2 i - u) w)^(-1 - n) Sum[2^(l - n) (-d - s (2 i - u) - f (2 j - v))^(-l + n) (d + s (2 i - u) + f (2 j - v) + 2 (b + c (2 j - v) + (2 i - u) w) z)^(1 + l) (-((d + s (2 i - u) + f (2 j - v) + 2 (b + c (2 j - v) + (2 i - u) w) z)^2/(b + c (2 j - v) + (2 i - u) w)))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + s (2 i - u) + f (2 j - v) + 2 (b + c (2 j - v) + (2 i - u) w) z)^2/(4 (b + c (2 j - v) + (2 i - u) w)))], {l, 0, n}] + E^(e + t (2 i - u) + (I Pi u)/2 + g (-2 j + v) - (d + s (2 i - u) + f (-2 j + v))^2/(4 (b + c (-2 j + v) + (2 i - u) w))) (b + c (-2 j + v) + (2 i - u) w)^(-1 - n) Sum[2^(l - n) (-d - s (2 i - u) - f (-2 j + v))^(-l + n) (d + s (2 i - u) + f (-2 j + v) + 2 (b + c (-2 j + v) + (2 i - u) w) z)^(1 + l) (-((d + s (2 i - u) + f (-2 j + v) + 2 (b + c (-2 j + v) + (2 i - u) w) z)^2/(b + c (-2 j + v) + (2 i - u) w)))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + s (2 i - u) + f (-2 j + v) + 2 (b + c (-2 j + v) + (2 i - u) w) z)^2/(4 (b + c (-2 j + v) + (2 i - u) w)))], {l, 0, n}] + E^(e - (I Pi u)/2 + t (-2 i + u) + g (2 j - v) - (d + s (-2 i + u) + f (2 j - v))^2/(4 (b + c (2 j - v) + (-2 i + u) w))) (b + c (2 j - v) + (-2 i + u) w)^(-1 - n) Sum[2^(l - n) (-d - s (-2 i + u) - f (2 j - v))^(-l + n) (d + s (-2 i + u) + f (2 j - v) + 2 (b + c (2 j - v) + (-2 i + u) w) z)^(1 + l) (-((d + s (-2 i + u) + f (2 j - v) + 2 (b + c (2 j - v) + (-2 i + u) w) z)^2/(b + c (2 j - v) + (-2 i + u) w)))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + s (-2 i + u) + f (2 j - v) + 2 (b + c (2 j - v) + (-2 i + u) w) z)^2/(4 (b + c (2 j - v) + (-2 i + u) w)))], {l, 0, n}] + E^(e - (I Pi u)/2 + t (-2 i + u) + g (-2 j + v) - (d + s (-2 i + u) + f (-2 j + v))^2/(4 (b + c (-2 j + v) + (-2 i + u) w))) (b + c (-2 j + v) + (-2 i + u) w)^(-1 - n) Sum[2^(l - n) (-d - s (-2 i + u) - f (-2 j + v))^(-l + n) (d + s (-2 i + u) + f (-2 j + v) + 2 (b + c (-2 j + v) + (-2 i + u) w) z)^(1 + l) (-((d + s (-2 i + u) + f (-2 j + v) + 2 (b + c (-2 j + v) + (-2 i + u) w) z)^2/(b + c (-2 j + v) + (-2 i + u) w)))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + s (-2 i + u) + f (-2 j + v) + 2 (b + c (-2 j + v) + (-2 i + u) w) z)^2/(4 (b + c (-2 j + v) + (-2 i + u) w)))], {l, 0, n}]), {i, 0, Floor[(1/2) (-1 + u)]}], {j, 0, Floor[(1/2) (-1 + v)]}] - I^u 2^(-1 - m - u - v) Sum[Binomial[v, k] Sum[Binomial[m, j] Sum[(-1)^i Binomial[u, i] (E^(e + I (2 j - m) q + t (2 i - u) + (I Pi u)/2 + g (2 k - v) - (d + I (2 j - m) p + s (2 i - u) + f (2 k - v))^2/(4 (b + I a (2 j - m) + c (2 k - v) + (2 i - u) w))) (b + I a (2 j - m) + c (2 k - v) + (2 i - u) w)^(-1 - n) Sum[2^(l - n) (-d - I (2 j - m) p - s (2 i - u) - f (2 k - v))^( -l + n) (d + I (2 j - m) p + s (2 i - u) + f (2 k - v) + 2 (b + I a (2 j - m) + c (2 k - v) + (2 i - u) w) z)^(1 + l) (-((d + I (2 j - m) p + s (2 i - u) + f (2 k - v) + 2 (b + I a (2 j - m) + c (2 k - v) + (2 i - u) w) z)^2/ (b + I a (2 j - m) + c (2 k - v) + (2 i - u) w)))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + I (2 j - m) p + s (2 i - u) + f (2 k - v) + 2 (b + I a (2 j - m) + c (2 k - v) + (2 i - u) w) z)^2/ (4 (b + I a (2 j - m) + c (2 k - v) + (2 i - u) w)))], {l, 0, n}] + E^(e + I (-2 j + m) q + t (2 i - u) + (I Pi u)/2 + g (2 k - v) - (d + I (-2 j + m) p + s (2 i - u) + f (2 k - v))^ 2/(4 (b + I a (-2 j + m) + c (2 k - v) + (2 i - u) w))) (b + I a (-2 j + m) + c (2 k - v) + (2 i - u) w)^(-1 - n) Sum[2^(l - n) (-d - I (-2 j + m) p - s (2 i - u) - f (2 k - v))^( -l + n) (d + I (-2 j + m) p + s (2 i - u) + f (2 k - v) + 2 (b + I a (-2 j + m) + c (2 k - v) + (2 i - u) w) z)^(1 + l) (-((d + I (-2 j + m) p + s (2 i - u) + f (2 k - v) + 2 (b + I a (-2 j + m) + c (2 k - v) + (2 i - u) w) z)^2/ (b + I a (-2 j + m) + c (2 k - v) + (2 i - u) w)))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + I (-2 j + m) p + s (2 i - u) + f (2 k - v) + 2 (b + I a (-2 j + m) + c (2 k - v) + (2 i - u) w) z)^2/ (4 (b + I a (-2 j + m) + c (2 k - v) + (2 i - u) w)))], {l, 0, n}] + E^(e + I (2 j - m) q + t (2 i - u) + (I Pi u)/2 + g (-2 k + v) - (d + I (2 j - m) p + s (2 i - u) + f (-2 k + v))^ 2/(4 (b + I a (2 j - m) + c (-2 k + v) + (2 i - u) w))) (b + I a (2 j - m) + c (-2 k + v) + (2 i - u) w)^(-1 - n) Sum[2^(l - n) (-d - I (2 j - m) p - s (2 i - u) - f (-2 k + v))^( -l + n) (d + I (2 j - m) p + s (2 i - u) + f (-2 k + v) + 2 (b + I a (2 j - m) + c (-2 k + v) + (2 i - u) w) z)^(1 + l) (-((d + I (2 j - m) p + s (2 i - u) + f (-2 k + v) + 2 (b + I a (2 j - m) + c (-2 k + v) + (2 i - u) w) z)^2/ (b + I a (2 j - m) + c (-2 k + v) + (2 i - u) w)))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + I (2 j - m) p + s (2 i - u) + f (-2 k + v) + 2 (b + I a (2 j - m) + c (-2 k + v) + (2 i - u) w) z)^2/ (4 (b + I a (2 j - m) + c (-2 k + v) + (2 i - u) w)))], {l, 0, n}] + E^(e + I (-2 j + m) q + t (2 i - u) + (I Pi u)/2 + g (-2 k + v) - (d + I (-2 j + m) p + s (2 i - u) + f (-2 k + v))^2/(4 (b + I a (-2 j + m) + c (-2 k + v) + (2 i - u) w))) (b + I a (-2 j + m) + c (-2 k + v) + (2 i - u) w)^(-1 - n) Sum[2^(l - n) (-d - I (-2 j + m) p - s (2 i - u) - f (-2 k + v))^(-l + n) (d + I (-2 j + m) p + s (2 i - u) + f (-2 k + v) + 2 (b + I a (-2 j + m) + c (-2 k + v) + (2 i - u) w) z)^(1 + l) (-((d + I (-2 j + m) p + s (2 i - u) + f (-2 k + v) + 2 (b + I a (-2 j + m) + c (-2 k + v) + (2 i - u) w) z)^2/ (b + I a (-2 j + m) + c (-2 k + v) + (2 i - u) w)))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + I (-2 j + m) p + s (2 i - u) + f (-2 k + v) + 2 (b + I a (-2 j + m) + c (-2 k + v) + (2 i - u) w) z)^2/ (4 (b + I a (-2 j + m) + c (-2 k + v) + (2 i - u) w)))], {l, 0, n}] + E^(e + I (2 j - m) q - (I Pi u)/2 + t (-2 i + u) + g (2 k - v) - (d + I (2 j - m) p + s (-2 i + u) + f (2 k - v))^ 2/(4 (b + I a (2 j - m) + c (2 k - v) + (-2 i + u) w))) (b + I a (2 j - m) + c (2 k - v) + (-2 i + u) w)^(-1 - n) Sum[2^(l - n) (-d - I (2 j - m) p - s (-2 i + u) - f (2 k - v))^( -l + n) (d + I (2 j - m) p + s (-2 i + u) + f (2 k - v) + 2 (b + I a (2 j - m) + c (2 k - v) + (-2 i + u) w) z)^(1 + l) (-((d + I (2 j - m) p + s (-2 i + u) + f (2 k - v) + 2 (b + I a (2 j - m) + c (2 k - v) + (-2 i + u) w) z)^2/ (b + I a (2 j - m) + c (2 k - v) + (-2 i + u) w)))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + I (2 j - m) p + s (-2 i + u) + f (2 k - v) + 2 (b + I a (2 j - m) + c (2 k - v) + (-2 i + u) w) z)^2/ (4 (b + I a (2 j - m) + c (2 k - v) + (-2 i + u) w)))], {l, 0, n}] + E^(e + I (-2 j + m) q - (I Pi u)/2 + t (-2 i + u) + g (2 k - v) - (d + I (-2 j + m) p + s (-2 i + u) + f (2 k - v))^ 2/(4 (b + I a (-2 j + m) + c (2 k - v) + (-2 i + u) w))) (b + I a (-2 j + m) + c (2 k - v) + (-2 i + u) w)^(-1 - n) Sum[2^(l - n) (-d - I (-2 j + m) p - s (-2 i + u) - f (2 k - v))^( -l + n) (d + I (-2 j + m) p + s (-2 i + u) + f (2 k - v) + 2 (b + I a (-2 j + m) + c (2 k - v) + (-2 i + u) w) z)^(1 + l) (-((d + I (-2 j + m) p + s (-2 i + u) + f (2 k - v) + 2 (b + I a (-2 j + m) + c (2 k - v) + (-2 i + u) w) z)^2/ (b + I a (-2 j + m) + c (2 k - v) + (-2 i + u) w)))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + I (-2 j + m) p + s (-2 i + u) + f (2 k - v) + 2 (b + I a (-2 j + m) + c (2 k - v) + (-2 i + u) w) z)^2/ (4 (b + I a (-2 j + m) + c (2 k - v) + (-2 i + u) w)))], {l, 0, n}] + E^(e + I (2 j - m) q - (I Pi u)/2 + t (-2 i + u) + g (-2 k + v) - (d + I (2 j - m) p + s (-2 i + u) + f (-2 k + v))^2/(4 (b + I a (2 j - m) + c (-2 k + v) + (-2 i + u) w))) (b + I a (2 j - m) + c (-2 k + v) + (-2 i + u) w)^(-1 - n) Sum[2^(l - n) (-d - I (2 j - m) p - s (-2 i + u) - f (-2 k + v))^(-l + n) (d + I (2 j - m) p + s (-2 i + u) + f (-2 k + v) + 2 (b + I a (2 j - m) + c (-2 k + v) + (-2 i + u) w) z)^(1 + l) (-((d + I (2 j - m) p + s (-2 i + u) + f (-2 k + v) + 2 (b + I a (2 j - m) + c (-2 k + v) + (-2 i + u) w) z)^2/ (b + I a (2 j - m) + c (-2 k + v) + (-2 i + u) w)))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + I (2 j - m) p + s (-2 i + u) + f (-2 k + v) + 2 (b + I a (2 j - m) + c (-2 k + v) + (-2 i + u) w) z)^2/ (4 (b + I a (2 j - m) + c (-2 k + v) + (-2 i + u) w)))], {l, 0, n}] + E^(e + I (-2 j + m) q - (I Pi u)/2 + t (-2 i + u) + g (-2 k + v) - (d + I (-2 j + m) p + s (-2 i + u) + f (-2 k + v))^2/(4 (b + I a (-2 j + m) + c (-2 k + v) + (-2 i + u) w))) (b + I a (-2 j + m) + c (-2 k + v) + (-2 i + u) w)^(-1 - n) Sum[2^(l - n) (-d - I (-2 j + m) p - s (-2 i + u) - f (-2 k + v))^(-l + n) (d + I (-2 j + m) p + s (-2 i + u) + f (-2 k + v) + 2 (b + I a (-2 j + m) + c (-2 k + v) + (-2 i + u) w) z)^(1 + l) (-((d + I (-2 j + m) p + s (-2 i + u) + f (-2 k + v) + 2 (b + I a (-2 j + m) + c (-2 k + v) + (-2 i + u) w) z)^2/ (b + I a (-2 j + m) + c (-2 k + v) + (-2 i + u) w)))^((1/2) (-1 - l)) Binomial[n, l] Gamma[(1 + l)/2, -((d + I (-2 j + m) p + s (-2 i + u) + f (-2 k + v) + 2 (b + I a (-2 j + m) + c (-2 k + v) + (-2 i + u) w) z)^2/ (4 (b + I a (-2 j + m) + c (-2 k + v) + (-2 i + u) w)))], {l, 0, n}]), {i, 0, Floor[(1/2) (-1 + u)]}], {j, 0, Floor[(1/2) (-1 + m)]}], {k, 0, Floor[(1/2) (-1 + v)]}] /; Element[n, Integers] && n >= 0 && Element[m, Integers] && m > 0 && Element[u, Integers] && u > 0 && Element[v, Integers] && v > 0

 Standard Form

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 MathML Form

 z n b z 2 + d z + e cos m ( a z 2 + p z + q ) sinh u ( w z 2 + s z + t ) cosh v ( c z 2 + f z + g ) z 2 - m - u - v - 1 e - d 2 4 b ( - u ) ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( u u 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["u", Identity]], List[TagBox[FractionBox["u", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) ( 1 - u mod 2 \$CellContext`u 2 ) ( 1 - v mod 2 \$CellContext`v 2 ) b - n - 1 l = 0 n 2 l - n ( - d ) n - l ( d + 2 b z ) l + 1 ( - ( d + 2 b z ) 2 b ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + 2 b z ) 2 4 b ) - u 2 - m - u - v - 1 ( u u 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["u", Identity]], List[TagBox[FractionBox["u", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - u mod 2 \$CellContext`u 2 ) ( 1 - v mod 2 \$CellContext`v 2 ) j = 0 m - 1 2 ( m j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( d + ( 2 j - m ) p ) 2 4 ( b + a ( 2 j - m ) ) + e + ( 2 j - m ) q ( b + a ( 2 j - m ) ) - n - 1 l = 0 n 2 l - n ( - d - ( 2 j - m ) p ) n - l ( d + ( 2 j - m ) p + 2 ( b + a ( 2 j - m ) ) z ) l + 1 ( - ( d + ( 2 j - m ) p + 2 ( b + a ( 2 j - m ) ) z ) 2 b + a ( 2 j - m ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + ( 2 j - m ) p + 2 ( b + a ( 2 j - m ) ) z ) 2 4 ( b + a ( 2 j - m ) ) ) + - ( d + ( m - 2 j ) p ) 2 4 ( b + a ( m - 2 j ) ) + e + ( m - 2 j ) q ( b + a ( m - 2 j ) ) - n - 1 l = 0 n 2 l - n ( - d - ( m - 2 j ) p ) n - l ( d + ( m - 2 j ) p + 2 ( b + a ( m - 2 j ) ) z ) l + 1 ( - ( d + ( m - 2 j ) p + 2 ( b + a ( m - 2 j ) ) z ) 2 b + a ( m - 2 j ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + ( m - 2 j ) p + 2 ( b + a ( m - 2 j ) ) z ) 2 4 ( b + a ( m - 2 j ) ) ) ) - u 2 - m - u - v - 1 ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( u u 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["u", Identity]], List[TagBox[FractionBox["u", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) ( 1 - u mod 2 \$CellContext`u 2 ) j = 0 v - 1 2 ( v j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( d + f ( 2 j - v ) ) 2 4 ( b + c ( 2 j - v ) ) + e + g ( 2 j - v ) ( b + c ( 2 j - v ) ) - n - 1 l = 0 n 2 l - n ( - d - f ( 2 j - v ) ) n - l ( d + f ( 2 j - v ) + 2 ( b + c ( 2 j - v ) ) z ) l + 1 ( - ( d + f ( 2 j - v ) + 2 ( b + c ( 2 j - v ) ) z ) 2 b + c ( 2 j - v ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + f ( 2 j - v ) + 2 ( b + c ( 2 j - v ) ) z ) 2 4 ( b + c ( 2 j - v ) ) ) + - ( d + f ( v - 2 j ) ) 2 4 ( b + c ( v - 2 j ) ) + e + g ( v - 2 j ) ( b + c ( v - 2 j ) ) - n - 1 l = 0 n 2 l - n ( - d - f ( v - 2 j ) ) n - l ( d + f ( v - 2 j ) + 2 ( b + c ( v - 2 j ) ) z ) l + 1 ( - ( d + f ( v - 2 j ) + 2 ( b + c ( v - 2 j ) ) z ) 2 b + c ( v - 2 j ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + f ( v - 2 j ) + 2 ( b + c ( v - 2 j ) ) z ) 2 4 ( b + c ( v - 2 j ) ) ) ) - u 2 - m - u - v - 1 ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) ( 1 - v mod 2 \$CellContext`v 2 ) i = 0 u - 1 2 ( - 1 ) i ( u i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["u", Identity]], List[TagBox["i", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( d + s ( 2 i - u ) ) 2 4 ( b + ( 2 i - u ) w ) + e + t ( 2 i - u ) + π u 2 ( b + ( 2 i - u ) w ) - n - 1 l = 0 n 2 l - n ( - d - s ( 2 i - u ) ) n - l ( d + s ( 2 i - u ) + 2 ( b + ( 2 i - u ) w ) z ) l + 1 ( - ( d + s ( 2 i - u ) + 2 ( b + ( 2 i - u ) w ) z ) 2 b + ( 2 i - u ) w ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + s ( 2 i - u ) + 2 ( b + ( 2 i - u ) w ) z ) 2 4 ( b + ( 2 i - u ) w ) ) + - ( d + s ( u - 2 i ) ) 2 4 ( b + ( u - 2 i ) w ) + e + t ( u - 2 i ) - π u 2 ( b + ( u - 2 i ) w ) - n - 1 l = 0 n 2 l - n ( - d - s ( u - 2 i ) ) n - l ( d + s ( u - 2 i ) + 2 ( b + ( u - 2 i ) w ) z ) l + 1 ( - ( d + s ( u - 2 i ) + 2 ( b + ( u - 2 i ) w ) z ) 2 b + ( u - 2 i ) w ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + s ( u - 2 i ) + 2 ( b + ( u - 2 i ) w ) z ) 2 4 ( b + ( u - 2 i ) w ) ) ) - u 2 - m - u - v - 1 ( u u 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["u", Identity]], List[TagBox[FractionBox["u", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - u mod 2 \$CellContext`u 2 ) k = 0 m - 1 2 ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] j = 0 v - 1 2 ( v j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( d + ( 2 k - m ) p + f ( 2 j - v ) ) 2 4 ( b + a ( 2 k - m ) + c ( 2 j - v ) ) + e + ( 2 k - m ) q + g ( 2 j - v ) ( b + a ( 2 k - m ) + c ( 2 j - v ) ) - n - 1 l = 0 n 2 l - n ( - d - ( 2 k - m ) p - f ( 2 j - v ) ) n - l ( d + ( 2 k - m ) p + f ( 2 j - v ) + 2 ( b + a ( 2 k - m ) + c ( 2 j - v ) ) z ) l + 1 ( - ( d + ( 2 k - m ) p + f ( 2 j - v ) + 2 ( b + a ( 2 k - m ) + c ( 2 j - v ) ) z ) 2 / ( b + a ( 2 k - m ) + c ( 2 j - v ) ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + ( 2 k - m ) p + f ( 2 j - v ) + 2 ( b + a ( 2 k - m ) + c ( 2 j - v ) ) z ) 2 / ( 4 ( b + a ( 2 k - m ) + c ( 2 j - v ) ) ) ) + - ( d + ( m - 2 k ) p + f ( 2 j - v ) ) 2 4 ( b + a ( m - 2 k ) + c ( 2 j - v ) ) + e + ( m - 2 k ) q + g ( 2 j - v ) ( b + a ( m - 2 k ) + c ( 2 j - v ) ) - n - 1 l = 0 n 2 l - n ( - d - ( m - 2 k ) p - f ( 2 j - v ) ) n - l ( d + ( m - 2 k ) p + f ( 2 j - v ) + 2 ( b + a ( m - 2 k ) + c ( 2 j - v ) ) z ) l + 1 ( - ( d + ( m - 2 k ) p + f ( 2 j - v ) + 2 ( b + a ( m - 2 k ) + c ( 2 j - v ) ) z ) 2 / ( b + a ( m - 2 k ) + c ( 2 j - v ) ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + ( m - 2 k ) p + f ( 2 j - v ) + 2 ( b + a ( m - 2 k ) + c ( 2 j - v ) ) z ) 2 / ( 4 ( b + a ( m - 2 k ) + c ( 2 j - v ) ) ) ) + - ( d + ( 2 k - m ) p + f ( v - 2 j ) ) 2 4 ( b + a ( 2 k - m ) + c ( v - 2 j ) ) + e + ( 2 k - m ) q + g ( v - 2 j ) ( b + a ( 2 k - m ) + c ( v - 2 j ) ) - n - 1 l = 0 n 2 l - n ( - d - ( 2 k - m ) p - f ( v - 2 j ) ) n - l ( d + ( 2 k - m ) p + f ( v - 2 j ) + 2 ( b + a ( 2 k - m ) + c ( v - 2 j ) ) z ) l + 1 ( - ( d + ( 2 k - m ) p + f ( v - 2 j ) + 2 ( b + a ( 2 k - m ) + c ( v - 2 j ) ) z ) 2 / ( b + a ( 2 k - m ) + c ( v - 2 j ) ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + ( 2 k - m ) p + f ( v - 2 j ) + 2 ( b + a ( 2 k - m ) + c ( v - 2 j ) ) z ) 2 / ( 4 ( b + a ( 2 k - m ) + c ( v - 2 j ) ) ) ) + - ( d + ( m - 2 k ) p + f ( v - 2 j ) ) 2 4 ( b + a ( m - 2 k ) + c ( v - 2 j ) ) + e + ( m - 2 k ) q + g ( v - 2 j ) ( b + a ( m - 2 k ) + c ( v - 2 j ) ) - n - 1 l = 0 n 2 l - n ( - d - ( m - 2 k ) p - f ( v - 2 j ) ) n - l ( d + ( m - 2 k ) p + f ( v - 2 j ) + 2 ( b + a ( m - 2 k ) + c ( v - 2 j ) ) z ) l + 1 ( - ( d + ( m - 2 k ) p + f ( v - 2 j ) + 2 ( b + a ( m - 2 k ) + c ( v - 2 j ) ) z ) 2 / ( b + a ( m - 2 k ) + c ( v - 2 j ) ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + ( m - 2 k ) p + f ( v - 2 j ) + 2 ( b + a ( m - 2 k ) + c ( v - 2 j ) ) z ) 2 / ( 4 ( b + a ( m - 2 k ) + c ( v - 2 j ) ) ) ) ) - u 2 - m - u - v - 1 ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - v mod 2 \$CellContext`v 2 ) j = 0 m - 1 2 ( m j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] i = 0 u - 1 2 ( - 1 ) i ( u i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["u", Identity]], List[TagBox["i", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( d + ( 2 j - m ) p + s ( 2 i - u ) ) 2 4 ( b + a ( 2 j - m ) + ( 2 i - u ) w ) + e + ( 2 j - m ) q + t ( 2 i - u ) + π u 2 ( b + a ( 2 j - m ) + ( 2 i - u ) w ) - n - 1 l = 0 n 2 l - n ( - d - ( 2 j - m ) p - s ( 2 i - u ) ) n - l ( d + ( 2 j - m ) p + s ( 2 i - u ) + 2 ( b + a ( 2 j - m ) + ( 2 i - u ) w ) z ) l + 1 ( - ( d + ( 2 j - m ) p + s ( 2 i - u ) + 2 ( b + a ( 2 j - m ) + ( 2 i - u ) w ) z ) 2 / ( b + a ( 2 j - m ) + ( 2 i - u ) w ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + ( 2 j - m ) p + s ( 2 i - u ) + 2 ( b + a ( 2 j - m ) + ( 2 i - u ) w ) z ) 2 / ( 4 ( b + a ( 2 j - m ) + ( 2 i - u ) w ) ) ) + - ( d + ( m - 2 j ) p + s ( 2 i - u ) ) 2 4 ( b + a ( m - 2 j ) + ( 2 i - u ) w ) + e + ( m - 2 j ) q + t ( 2 i - u ) + π u 2 ( b + a ( m - 2 j ) + ( 2 i - u ) w ) - n - 1 l = 0 n 2 l - n ( - d - ( m - 2 j ) p - s ( 2 i - u ) ) n - l ( d + ( m - 2 j ) p + s ( 2 i - u ) + 2 ( b + a ( m - 2 j ) + ( 2 i - u ) w ) z ) l + 1 ( - ( d + ( m - 2 j ) p + s ( 2 i - u ) + 2 ( b + a ( m - 2 j ) + ( 2 i - u ) w ) z ) 2 / ( b + a ( m - 2 j ) + ( 2 i - u ) w ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + ( m - 2 j ) p + s ( 2 i - u ) + 2 ( b + a ( m - 2 j ) + ( 2 i - u ) w ) z ) 2 / ( 4 ( b + a ( m - 2 j ) + ( 2 i - u ) w ) ) ) + - ( d + ( 2 j - m ) p + s ( u - 2 i ) ) 2 4 ( b + a ( 2 j - m ) + ( u - 2 i ) w ) + e + ( 2 j - m ) q + t ( u - 2 i ) - π u 2 ( b + a ( 2 j - m ) + ( u - 2 i ) w ) - n - 1 l = 0 n 2 l - n ( - d - ( 2 j - m ) p - s ( u - 2 i ) ) n - l ( d + ( 2 j - m ) p + s ( u - 2 i ) + 2 ( b + a ( 2 j - m ) + ( u - 2 i ) w ) z ) l + 1 ( - ( d + ( 2 j - m ) p + s ( u - 2 i ) + 2 ( b + a ( 2 j - m ) + ( u - 2 i ) w ) z ) 2 / ( b + a ( 2 j - m ) + ( u - 2 i ) w ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + ( 2 j - m ) p + s ( u - 2 i ) + 2 ( b + a ( 2 j - m ) + ( u - 2 i ) w ) z ) 2 / ( 4 ( b + a ( 2 j - m ) + ( u - 2 i ) w ) ) ) + - ( d + ( m - 2 j ) p + s ( u - 2 i ) ) 2 4 ( b + a ( m - 2 j ) + ( u - 2 i ) w ) + e + ( m - 2 j ) q + t ( u - 2 i ) - π u 2 ( b + a ( m - 2 j ) + ( u - 2 i ) w ) - n - 1 l = 0 n 2 l - n ( - d - ( m - 2 j ) p - s ( u - 2 i ) ) n - l ( d + ( m - 2 j ) p + s ( u - 2 i ) + 2 ( b + a ( m - 2 j ) + ( u - 2 i ) w ) z ) l + 1 ( - ( d + ( m - 2 j ) p + s ( u - 2 i ) + 2 ( b + a ( m - 2 j ) + ( u - 2 i ) w ) z ) 2 / ( b + a ( m - 2 j ) + ( u - 2 i ) w ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + ( m - 2 j ) p + s ( u - 2 i ) + 2 ( b + a ( m - 2 j ) + ( u - 2 i ) w ) z ) 2 / ( 4 ( b + a ( m - 2 j ) + ( u - 2 i ) w ) ) ) ) - u 2 - m - u - v - 1 ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) j = 0 v - 1 2 ( v j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] i = 0 u - 1 2 ( - 1 ) i ( u i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["u", Identity]], List[TagBox["i", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( d + s ( 2 i - u ) + f ( 2 j - v ) ) 2 4 ( b + c ( 2 j - v ) + ( 2 i - u ) w ) + e + t ( 2 i - u ) + π u 2 + g ( 2 j - v ) ( b + c ( 2 j - v ) + ( 2 i - u ) w ) - n - 1 l = 0 n 2 l - n ( - d - s ( 2 i - u ) - f ( 2 j - v ) ) n - l ( d + s ( 2 i - u ) + f ( 2 j - v ) + 2 ( b + c ( 2 j - v ) + ( 2 i - u ) w ) z ) l + 1 ( - ( d + s ( 2 i - u ) + f ( 2 j - v ) + 2 ( b + c ( 2 j - v ) + ( 2 i - u ) w ) z ) 2 / ( b + c ( 2 j - v ) + ( 2 i - u ) w ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + s ( 2 i - u ) + f ( 2 j - v ) + 2 ( b + c ( 2 j - v ) + ( 2 i - u ) w ) z ) 2 4 ( b + c ( 2 j - v ) + ( 2 i - u ) w ) ) + - ( d + s ( 2 i - u ) + f ( v - 2 j ) ) 2 4 ( b + c ( v - 2 j ) + ( 2 i - u ) w ) + e + t ( 2 i - u ) + π u 2 + g ( v - 2 j ) ( b + c ( v - 2 j ) + ( 2 i - u ) w ) - n - 1 l = 0 n 2 l - n ( - d - s ( 2 i - u ) - f ( v - 2 j ) ) n - l ( d + s ( 2 i - u ) + f ( v - 2 j ) + 2 ( b + c ( v - 2 j ) + ( 2 i - u ) w ) z ) l + 1 ( - ( d + s ( 2 i - u ) + f ( v - 2 j ) + 2 ( b + c ( v - 2 j ) + ( 2 i - u ) w ) z ) 2 / ( b + c ( v - 2 j ) + ( 2 i - u ) w ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + s ( 2 i - u ) + f ( v - 2 j ) + 2 ( b + c ( v - 2 j ) + ( 2 i - u ) w ) z ) 2 4 ( b + c ( v - 2 j ) + ( 2 i - u ) w ) ) + - ( d + s ( u - 2 i ) + f ( 2 j - v ) ) 2 4 ( b + c ( 2 j - v ) + ( u - 2 i ) w ) + e + t ( u - 2 i ) + g ( 2 j - v ) - π u 2 ( b + c ( 2 j - v ) + ( u - 2 i ) w ) - n - 1 l = 0 n 2 l - n ( - d - s ( u - 2 i ) - f ( 2 j - v ) ) n - l ( d + s ( u - 2 i ) + f ( 2 j - v ) + 2 ( b + c ( 2 j - v ) + ( u - 2 i ) w ) z ) l + 1 ( - ( d + s ( u - 2 i ) + f ( 2 j - v ) + 2 ( b + c ( 2 j - v ) + ( u - 2 i ) w ) z ) 2 / ( b + c ( 2 j - v ) + ( u - 2 i ) w ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + s ( u - 2 i ) + f ( 2 j - v ) + 2 ( b + c ( 2 j - v ) + ( u - 2 i ) w ) z ) 2 4 ( b + c ( 2 j - v ) + ( u - 2 i ) w ) ) + - ( d + s ( u - 2 i ) + f ( v - 2 j ) ) 2 4 ( b + c ( v - 2 j ) + ( u - 2 i ) w ) + e + t ( u - 2 i ) + g ( v - 2 j ) - π u 2 ( b + c ( v - 2 j ) + ( u - 2 i ) w ) - n - 1 l = 0 n 2 l - n ( - d - s ( u - 2 i ) - f ( v - 2 j ) ) n - l ( d + s ( u - 2 i ) + f ( v - 2 j ) + 2 ( b + c ( v - 2 j ) + ( u - 2 i ) w ) z ) l + 1 ( - ( d + s ( u - 2 i ) + f ( v - 2 j ) + 2 ( b + c ( v - 2 j ) + ( u - 2 i ) w ) z ) 2 / ( b + c ( v - 2 j ) + ( u - 2 i ) w ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + s ( u - 2 i ) + f ( v - 2 j ) + 2 ( b + c ( v - 2 j ) + ( u - 2 i ) w ) z ) 2 4 ( b + c ( v - 2 j ) + ( u - 2 i ) w ) ) ) - u 2 - m - u - v - 1 k = 0 v - 1 2 ( v k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] j = 0 m - 1 2 ( m j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] i = 0 u - 1 2 ( - 1 ) i ( u i ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["u", Identity]], List[TagBox["i", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( d + ( 2 j - m ) p + s ( 2 i - u ) + f ( 2 k - v ) ) 2 4 ( b + a ( 2 j - m ) + c ( 2 k - v ) + ( 2 i - u ) w ) + e + ( 2 j - m ) q + t ( 2 i - u ) + π u 2 + g ( 2 k - v ) ( b + a ( 2 j - m ) + c ( 2 k - v ) + ( 2 i - u ) w ) - n - 1 l = 0 n 2 l - n ( - d - ( 2 j - m ) p - s ( 2 i - u ) - f ( 2 k - v ) ) n - l ( d + ( 2 j - m ) p + s ( 2 i - u ) + f ( 2 k - v ) + 2 ( b + a ( 2 j - m ) + c ( 2 k - v ) + ( 2 i - u ) w ) z ) l + 1 ( - ( d + ( 2 j - m ) p + s ( 2 i - u ) + f ( 2 k - v ) + 2 ( b + a ( 2 j - m ) + c ( 2 k - v ) + ( 2 i - u ) w ) z ) 2 / ( b + a ( 2 j - m ) + c ( 2 k - v ) + ( 2 i - u ) w ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + ( 2 j - m ) p + s ( 2 i - u ) + f ( 2 k - v ) + 2 ( b + a ( 2 j - m ) + c ( 2 k - v ) + ( 2 i - u ) w ) z ) 2 / ( 4 ( b + a ( 2 j - m ) + c ( 2 k - v ) + ( 2 i - u ) w ) ) ) + - ( d + ( m - 2 j ) p + s ( 2 i - u ) + f ( 2 k - v ) ) 2 4 ( b + a ( m - 2 j ) + c ( 2 k - v ) + ( 2 i - u ) w ) + e + ( m - 2 j ) q + t ( 2 i - u ) + π u 2 + g ( 2 k - v ) ( b + a ( m - 2 j ) + c ( 2 k - v ) + ( 2 i - u ) w ) - n - 1 l = 0 n 2 l - n ( - d - ( m - 2 j ) p - s ( 2 i - u ) - f ( 2 k - v ) ) n - l ( d + ( m - 2 j ) p + s ( 2 i - u ) + f ( 2 k - v ) + 2 ( b + a ( m - 2 j ) + c ( 2 k - v ) + ( 2 i - u ) w ) z ) l + 1 ( - ( d + ( m - 2 j ) p + s ( 2 i - u ) + f ( 2 k - v ) + 2 ( b + a ( m - 2 j ) + c ( 2 k - v ) + ( 2 i - u ) w ) z ) 2 / ( b + a ( m - 2 j ) + c ( 2 k - v ) + ( 2 i - u ) w ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + ( m - 2 j ) p + s ( 2 i - u ) + f ( 2 k - v ) + 2 ( b + a ( m - 2 j ) + c ( 2 k - v ) + ( 2 i - u ) w ) z ) 2 / ( 4 ( b + a ( m - 2 j ) + c ( 2 k - v ) + ( 2 i - u ) w ) ) ) + - ( d + ( 2 j - m ) p + s ( 2 i - u ) + f ( v - 2 k ) ) 2 4 ( b + a ( 2 j - m ) + c ( v - 2 k ) + ( 2 i - u ) w ) + e + ( 2 j - m ) q + t ( 2 i - u ) + π u 2 + g ( v - 2 k ) ( b + a ( 2 j - m ) + c ( v - 2 k ) + ( 2 i - u ) w ) - n - 1 l = 0 n 2 l - n ( - d - ( 2 j - m ) p - s ( 2 i - u ) - f ( v - 2 k ) ) n - l ( d + ( 2 j - m ) p + s ( 2 i - u ) + f ( v - 2 k ) + 2 ( b + a ( 2 j - m ) + c ( v - 2 k ) + ( 2 i - u ) w ) z ) l + 1 ( - ( d + ( 2 j - m ) p + s ( 2 i - u ) + f ( v - 2 k ) + 2 ( b + a ( 2 j - m ) + c ( v - 2 k ) + ( 2 i - u ) w ) z ) 2 / ( b + a ( 2 j - m ) + c ( v - 2 k ) + ( 2 i - u ) w ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + ( 2 j - m ) p + s ( 2 i - u ) + f ( v - 2 k ) + 2 ( b + a ( 2 j - m ) + c ( v - 2 k ) + ( 2 i - u ) w ) z ) 2 / ( 4 ( b + a ( 2 j - m ) + c ( v - 2 k ) + ( 2 i - u ) w ) ) ) + - ( d + ( m - 2 j ) p + s ( 2 i - u ) + f ( v - 2 k ) ) 2 4 ( b + a ( m - 2 j ) + c ( v - 2 k ) + ( 2 i - u ) w ) + e + ( m - 2 j ) q + t ( 2 i - u ) + π u 2 + g ( v - 2 k ) ( b + a ( m - 2 j ) + c ( v - 2 k ) + ( 2 i - u ) w ) - n - 1 l = 0 n 2 l - n ( - d - ( m - 2 j ) p - s ( 2 i - u ) - f ( v - 2 k ) ) n - l ( d + ( m - 2 j ) p + s ( 2 i - u ) + f ( v - 2 k ) + 2 ( b + a ( m - 2 j ) + c ( v - 2 k ) + ( 2 i - u ) w ) z ) l + 1 ( - ( d + ( m - 2 j ) p + s ( 2 i - u ) + f ( v - 2 k ) + 2 ( b + a ( m - 2 j ) + c ( v - 2 k ) + ( 2 i - u ) w ) z ) 2 / ( b + a ( m - 2 j ) + c ( v - 2 k ) + ( 2 i - u ) w ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + ( m - 2 j ) p + s ( 2 i - u ) + f ( v - 2 k ) + 2 ( b + a ( m - 2 j ) + c ( v - 2 k ) + ( 2 i - u ) w ) z ) 2 / ( 4 ( b + a ( m - 2 j ) + c ( v - 2 k ) + ( 2 i - u ) w ) ) ) + - ( d + ( 2 j - m ) p + s ( u - 2 i ) + f ( 2 k - v ) ) 2 4 ( b + a ( 2 j - m ) + c ( 2 k - v ) + ( u - 2 i ) w ) + e + ( 2 j - m ) q + t ( u - 2 i ) + g ( 2 k - v ) - π u 2 ( b + a ( 2 j - m ) + c ( 2 k - v ) + ( u - 2 i ) w ) - n - 1 l = 0 n 2 l - n ( - d - ( 2 j - m ) p - s ( u - 2 i ) - f ( 2 k - v ) ) n - l ( d + ( 2 j - m ) p + s ( u - 2 i ) + f ( 2 k - v ) + 2 ( b + a ( 2 j - m ) + c ( 2 k - v ) + ( u - 2 i ) w ) z ) l + 1 ( - ( d + ( 2 j - m ) p + s ( u - 2 i ) + f ( 2 k - v ) + 2 ( b + a ( 2 j - m ) + c ( 2 k - v ) + ( u - 2 i ) w ) z ) 2 / ( b + a ( 2 j - m ) + c ( 2 k - v ) + ( u - 2 i ) w ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + ( 2 j - m ) p + s ( u - 2 i ) + f ( 2 k - v ) + 2 ( b + a ( 2 j - m ) + c ( 2 k - v ) + ( u - 2 i ) w ) z ) 2 / ( 4 ( b + a ( 2 j - m ) + c ( 2 k - v ) + ( u - 2 i ) w ) ) ) + - ( d + ( m - 2 j ) p + s ( u - 2 i ) + f ( 2 k - v ) ) 2 4 ( b + a ( m - 2 j ) + c ( 2 k - v ) + ( u - 2 i ) w ) + e + ( m - 2 j ) q + t ( u - 2 i ) + g ( 2 k - v ) - π u 2 ( b + a ( m - 2 j ) + c ( 2 k - v ) + ( u - 2 i ) w ) - n - 1 l = 0 n 2 l - n ( - d - ( m - 2 j ) p - s ( u - 2 i ) - f ( 2 k - v ) ) n - l ( d + ( m - 2 j ) p + s ( u - 2 i ) + f ( 2 k - v ) + 2 ( b + a ( m - 2 j ) + c ( 2 k - v ) + ( u - 2 i ) w ) z ) l + 1 ( - ( d + ( m - 2 j ) p + s ( u - 2 i ) + f ( 2 k - v ) + 2 ( b + a ( m - 2 j ) + c ( 2 k - v ) + ( u - 2 i ) w ) z ) 2 / ( b + a ( m - 2 j ) + c ( 2 k - v ) + ( u - 2 i ) w ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + ( m - 2 j ) p + s ( u - 2 i ) + f ( 2 k - v ) + 2 ( b + a ( m - 2 j ) + c ( 2 k - v ) + ( u - 2 i ) w ) z ) 2 / ( 4 ( b + a ( m - 2 j ) + c ( 2 k - v ) + ( u - 2 i ) w ) ) ) + - ( d + ( 2 j - m ) p + s ( u - 2 i ) + f ( v - 2 k ) ) 2 4 ( b + a ( 2 j - m ) + c ( v - 2 k ) + ( u - 2 i ) w ) + e + ( 2 j - m ) q + t ( u - 2 i ) + g ( v - 2 k ) - π u 2 ( b + a ( 2 j - m ) + c ( v - 2 k ) + ( u - 2 i ) w ) - n - 1 l = 0 n 2 l - n ( - d - ( 2 j - m ) p - s ( u - 2 i ) - f ( v - 2 k ) ) n - l ( d + ( 2 j - m ) p + s ( u - 2 i ) + f ( v - 2 k ) + 2 ( b + a ( 2 j - m ) + c ( v - 2 k ) + ( u - 2 i ) w ) z ) l + 1 ( - ( d + ( 2 j - m ) p + s ( u - 2 i ) + f ( v - 2 k ) + 2 ( b + a ( 2 j - m ) + c ( v - 2 k ) + ( u - 2 i ) w ) z ) 2 / ( b + a ( 2 j - m ) + c ( v - 2 k ) + ( u - 2 i ) w ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + ( 2 j - m ) p + s ( u - 2 i ) + f ( v - 2 k ) + 2 ( b + a ( 2 j - m ) + c ( v - 2 k ) + ( u - 2 i ) w ) z ) 2 / ( 4 ( b + a ( 2 j - m ) + c ( v - 2 k ) + ( u - 2 i ) w ) ) ) + - ( d + ( m - 2 j ) p + s ( u - 2 i ) + f ( v - 2 k ) ) 2 4 ( b + a ( m - 2 j ) + c ( v - 2 k ) + ( u - 2 i ) w ) + e + ( m - 2 j ) q + t ( u - 2 i ) + g ( v - 2 k ) - π u 2 ( b + a ( m - 2 j ) + c ( v - 2 k ) + ( u - 2 i ) w ) - n - 1 l = 0 n 2 l - n ( - d - ( m - 2 j ) p - s ( u - 2 i ) - f ( v - 2 k ) ) n - l ( d + ( m - 2 j ) p + s ( u - 2 i ) + f ( v - 2 k ) + 2 ( b + a ( m - 2 j ) + c ( v - 2 k ) + ( u - 2 i ) w ) z ) l + 1 ( - ( d + ( m - 2 j ) p + s ( u - 2 i ) + f ( v - 2 k ) + 2 ( b + a ( m - 2 j ) + c ( v - 2 k ) + ( u - 2 i ) w ) z ) 2 / ( b + a ( m - 2 j ) + c ( v - 2 k ) + ( u - 2 i ) w ) ) 1 2 ( - l - 1 ) ( n l ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["l", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( l + 1 2 , - ( d + ( m - 2 j ) p + s ( u - 2 i ) + f ( v - 2 k ) + 2 ( b + a ( m - 2 j ) + c ( v - 2 k ) + ( u - 2 i ) w ) z ) 2 / ( 4 ( b + a ( m - 2 j ) + c ( v - 2 k ) + ( u - 2 i ) w ) ) ) ) /; n m + u + v + Condition z z n b z 2 d z e a z 2 p z q m w z 2 s z t u c z 2 f z g v 2 -1 m -1 u -1 v -1 e -1 d 2 4 b -1 -1 u Binomial m m 2 -1 Binomial u u 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`m 2 1 -1 \$CellContext`u 2 1 -1 \$CellContext`v 2 b -1 n -1 l 0 n 2 l -1 n -1 d n -1 l d 2 b z l 1 -1 d 2 b z 2 b -1 1 2 -1 l -1 Binomial n l Gamma l 1 2 -1 -1 d 2 b z 2 4 b -1 -1 u 2 -1 m -1 u -1 v -1 Binomial u u 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`u 2 1 -1 \$CellContext`v 2 j 0 m -1 2 -1 Binomial m j -1 d 2 j -1 m p 2 4 b a 2 j -1 m -1 e 2 j -1 m q b a 2 j -1 m -1 n -1 l 0 n 2 l -1 n -1 d -1 2 j -1 m p n -1 l d 2 j -1 m p 2 b a 2 j -1 m z l 1 -1 d 2 j -1 m p 2 b a 2 j -1 m z 2 b a 2 j -1 m -1 1 2 -1 l -1 Binomial n l Gamma l 1 2 -1 -1 d 2 j -1 m p 2 b a 2 j -1 m z 2 4 b a 2 j -1 m -1 -1 d m -1 2 j p 2 4 b a m -1 2 j -1 e m -1 2 j q b a m -1 2 j -1 n -1 l 0 n 2 l -1 n -1 d -1 m -1 2 j p n -1 l d m -1 2 j p 2 b a m -1 2 j z l 1 -1 d m -1 2 j p 2 b a m -1 2 j z 2 b a m -1 2 j -1 1 2 -1 l -1 Binomial n l Gamma l 1 2 -1 -1 d m -1 2 j p 2 b a m -1 2 j z 2 4 b a m -1 2 j -1 -1 u 2 -1 m -1 u -1 v -1 Binomial m m 2 -1 Binomial u u 2 -1 1 -1 \$CellContext`m 2 1 -1 \$CellContext`u 2 j 0 v -1 2 -1 Binomial v j -1 d f 2 j -1 v 2 4 b c 2 j -1 v -1 e g 2 j -1 v b c 2 j -1 v -1 n -1 l 0 n 2 l -1 n -1 d -1 f 2 j -1 v n -1 l d f 2 j -1 v 2 b c 2 j -1 v z l 1 -1 d f 2 j -1 v 2 b c 2 j -1 v z 2 b c 2 j -1 v -1 1 2 -1 l -1 Binomial n l Gamma l 1 2 -1 -1 d f 2 j -1 v 2 b c 2 j -1 v z 2 4 b c 2 j -1 v -1 -1 d f v -1 2 j 2 4 b c v -1 2 j -1 e g v -1 2 j b c v -1 2 j -1 n -1 l 0 n 2 l -1 n -1 d -1 f v -1 2 j n -1 l d f v -1 2 j 2 b c v -1 2 j z l 1 -1 d f v -1 2 j 2 b c v -1 2 j z 2 b c v -1 2 j -1 1 2 -1 l -1 Binomial n l Gamma l 1 2 -1 -1 d f v -1 2 j 2 b c v -1 2 j z 2 4 b c v -1 2 j -1 -1 u 2 -1 m -1 u -1 v -1 Binomial m m 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`m 2 1 -1 \$CellContext`v 2 i 0 u -1 2 -1 -1 i Binomial u i -1 d s 2 i -1 u 2 4 b 2 i -1 u w -1 e t 2 i -1 u u 2 -1 b 2 i -1 u w -1 n -1 l 0 n 2 l -1 n -1 d -1 s 2 i -1 u n -1 l d s 2 i -1 u 2 b 2 i -1 u w z l 1 -1 d s 2 i -1 u 2 b 2 i -1 u w z 2 b 2 i -1 u w -1 1 2 -1 l -1 Binomial n l Gamma l 1 2 -1 -1 d s 2 i -1 u 2 b 2 i -1 u w z 2 4 b 2 i -1 u w -1 -1 d s u -1 2 i 2 4 b u -1 2 i w -1 e t u -1 2 i -1 u 2 -1 b u -1 2 i w -1 n -1 l 0 n 2 l -1 n -1 d -1 s u -1 2 i n -1 l d s u -1 2 i 2 b u -1 2 i w z l 1 -1 d s u -1 2 i 2 b u -1 2 i w z 2 b u -1 2 i w -1 1 2 -1 l -1 Binomial n l Gamma l 1 2 -1 -1 d s u -1 2 i 2 b u -1 2 i w z 2 4 b u -1 2 i w -1 -1 u 2 -1 m -1 u -1 v -1 Binomial u u 2 -1 1 -1 \$CellContext`u 2 k 0 m -1 2 -1 Binomial m k j 0 v -1 2 -1 Binomial v j -1 d 2 k -1 m p f 2 j -1 v 2 4 b a 2 k -1 m c 2 j -1 v -1 e 2 k -1 m q g 2 j -1 v b a 2 k -1 m c 2 j -1 v -1 n -1 l 0 n 2 l -1 n -1 d -1 2 k -1 m p -1 f 2 j -1 v n -1 l d 2 k -1 m p f 2 j -1 v 2 b a 2 k -1 m c 2 j -1 v z l 1 -1 d 2 k -1 m p f 2 j -1 v 2 b a 2 k -1 m c 2 j -1 v z 2 b a 2 k -1 m c 2 j -1 v -1 1 2 -1 l -1 Binomial n l Gamma l 1 2 -1 -1 d 2 k -1 m p f 2 j -1 v 2 b a 2 k -1 m c 2 j -1 v z 2 4 b a 2 k -1 m c 2 j -1 v -1 -1 d m -1 2 k p f 2 j -1 v 2 4 b a m -1 2 k c 2 j -1 v -1 e m -1 2 k q g 2 j -1 v b a m -1 2 k c 2 j -1 v -1 n -1 l 0 n 2 l -1 n -1 d -1 m -1 2 k p -1 f 2 j -1 v n -1 l d m -1 2 k p f 2 j -1 v 2 b a m -1 2 k c 2 j -1 v z l 1 -1 d m -1 2 k p f 2 j -1 v 2 b a m -1 2 k c 2 j -1 v z 2 b a m -1 2 k c 2 j -1 v -1 1 2 -1 l -1 Binomial n l Gamma l 1 2 -1 -1 d m -1 2 k p f 2 j -1 v 2 b a m -1 2 k c 2 j -1 v z 2 4 b a m -1 2 k c 2 j -1 v -1 -1 d 2 k -1 m p f v -1 2 j 2 4 b a 2 k -1 m c v -1 2 j -1 e 2 k -1 m q g v -1 2 j b a 2 k -1 m c v -1 2 j -1 n -1 l 0 n 2 l -1 n -1 d -1 2 k -1 m p -1 f v -1 2 j n -1 l d 2 k -1 m p f v -1 2 j 2 b a 2 k -1 m c v -1 2 j z l 1 -1 d 2 k -1 m p f v -1 2 j 2 b a 2 k -1 m c v -1 2 j z 2 b a 2 k -1 m c v -1 2 j -1 1 2 -1 l -1 Binomial n l Gamma l 1 2 -1 -1 d 2 k -1 m p f v -1 2 j 2 b a 2 k -1 m c v -1 2 j z 2 4 b a 2 k -1 m c v -1 2 j -1 -1 d m -1 2 k p f v -1 2 j 2 4 b a m -1 2 k c v -1 2 j -1 e m -1 2 k q g v -1 2 j b a m -1 2 k c v -1 2 j -1 n -1 l 0 n 2 l -1 n -1 d -1 m -1 2 k p -1 f v -1 2 j n -1 l d m -1 2 k p f v -1 2 j 2 b a m -1 2 k c v -1 2 j z l 1 -1 d m -1 2 k p f v -1 2 j 2 b a m -1 2 k c v -1 2 j z 2 b a m -1 2 k c v -1 2 j -1 1 2 -1 l -1 Binomial n l Gamma l 1 2 -1 -1 d m -1 2 k p f v -1 2 j 2 b a m -1 2 k c v -1 2 j z 2 4 b a m -1 2 k c v -1 2 j -1 -1 u 2 -1 m -1 u -1 v -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 j 0 m -1 2 -1 Binomial m j i 0 u -1 2 -1 -1 i Binomial u i -1 d 2 j -1 m p s 2 i -1 u 2 4 b a 2 j -1 m 2 i -1 u w -1 e 2 j -1 m q t 2 i -1 u u 2 -1 b a 2 j -1 m 2 i -1 u w -1 n -1 l 0 n 2 l -1 n -1 d -1 2 j -1 m p -1 s 2 i -1 u n -1 l d 2 j -1 m p s 2 i -1 u 2 b a 2 j -1 m 2 i -1 u w z l 1 -1 d 2 j -1 m p s 2 i -1 u 2 b a 2 j -1 m 2 i -1 u w z 2 b a 2 j -1 m 2 i -1 u w -1 1 2 -1 l -1 Binomial n l Gamma l 1 2 -1 -1 d 2 j -1 m p s 2 i -1 u 2 b a 2 j -1 m 2 i -1 u w z 2 4 b a 2 j -1 m 2 i -1 u w -1 -1 d m -1 2 j p s 2 i -1 u 2 4 b a m -1 2 j 2 i -1 u w -1 e m -1 2 j q t 2 i -1 u u 2 -1 b a m -1 2 j 2 i -1 u w -1 n -1 l 0 n 2 l -1 n -1 d -1 m -1 2 j p -1 s 2 i -1 u n -1 l d m -1 2 j p s 2 i -1 u 2 b a m -1 2 j 2 i -1 u w z l 1 -1 d m -1 2 j p s 2 i -1 u 2 b a m -1 2 j 2 i -1 u w z 2 b a m -1 2 j 2 i -1 u w -1 1 2 -1 l -1 Binomial n l Gamma l 1 2 -1 -1 d m -1 2 j p s 2 i -1 u 2 b a m -1 2 j 2 i -1 u w z 2 4 b a m -1 2 j 2 i -1 u w -1 -1 d 2 j -1 m p s u -1 2 i 2 4 b a 2 j -1 m u -1 2 i w -1 e 2 j -1 m q t u -1 2 i -1 u 2 -1 b a 2 j -1 m u -1 2 i w -1 n -1 l 0 n 2 l -1 n -1 d -1 2 j -1 m p -1 s u -1 2 i n -1 l d 2 j -1 m p s u -1 2 i 2 b a 2 j -1 m u -1 2 i w z l 1 -1 d 2 j -1 m p s u -1 2 i 2 b a 2 j -1 m u -1 2 i w z 2 b a 2 j -1 m u -1 2 i w -1 1 2 -1 l -1 Binomial n l Gamma l 1 2 -1 -1 d 2 j -1 m p s u -1 2 i 2 b a 2 j -1 m u -1 2 i w z 2 4 b a 2 j -1 m u -1 2 i w -1 -1 d m -1 2 j p s u -1 2 i 2 4 b a m -1 2 j u -1 2 i w -1 e m -1 2 j q t u -1 2 i -1 u 2 -1 b a m -1 2 j u -1 2 i w -1 n -1 l 0 n 2 l -1 n -1 d -1 m -1 2 j p -1 s u -1 2 i n -1 l d m -1 2 j p s u -1 2 i 2 b a m -1 2 j u -1 2 i w z l 1 -1 d m -1 2 j p s u -1 2 i 2 b a m -1 2 j u -1 2 i w z 2 b a m -1 2 j u -1 2 i w -1 1 2 -1 l -1 Binomial n l Gamma l 1 2 -1 -1 d m -1 2 j p s u -1 2 i 2 b a m -1 2 j u -1 2 i w z 2 4 b a m -1 2 j u -1 2 i w -1 -1 u 2 -1 m -1 u -1 v -1 Binomial m m 2 -1 1 -1 \$CellContext`m 2 j 0 v -1 2 -1 Binomial v j i 0 u -1 2 -1 -1 i Binomial u i -1 d s 2 i -1 u f 2 j -1 v 2 4 b c 2 j -1 v 2 i -1 u w -1 e t 2 i -1 u u 2 -1 g 2 j -1 v b c 2 j -1 v 2 i -1 u w -1 n -1 l 0 n 2 l -1 n -1 d -1 s 2 i -1 u -1 f 2 j -1 v n -1 l d s 2 i -1 u f 2 j -1 v 2 b c 2 j -1 v 2 i -1 u w z l 1 -1 d s 2 i -1 u f 2 j -1 v 2 b c 2 j -1 v 2 i -1 u w z 2 b c 2 j -1 v 2 i -1 u w -1 1 2 -1 l -1 Binomial n l Gamma l 1 2 -1 -1 d s 2 i -1 u f 2 j -1 v 2 b c 2 j -1 v 2 i -1 u w z 2 4 b c 2 j -1 v 2 i -1 u w -1 -1 d s 2 i -1 u f v -1 2 j 2 4 b c v -1 2 j 2 i -1 u w -1 e t 2 i -1 u u 2 -1 g v -1 2 j b c v -1 2 j 2 i -1 u w -1 n -1 l 0 n 2 l -1 n -1 d -1 s 2 i -1 u -1 f v -1 2 j n -1 l d s 2 i -1 u f v -1 2 j 2 b c v -1 2 j 2 i -1 u w z l 1 -1 d s 2 i -1 u f v -1 2 j 2 b c v -1 2 j 2 i -1 u w z 2 b c v -1 2 j 2 i -1 u w -1 1 2 -1 l -1 Binomial n l Gamma l 1 2 -1 -1 d s 2 i -1 u f v -1 2 j 2 b c v -1 2 j 2 i -1 u w z 2 4 b c v -1 2 j 2 i -1 u w -1 -1 d s u -1 2 i f 2 j -1 v 2 4 b c 2 j -1 v u -1 2 i w -1 e t u -1 2 i g 2 j -1 v -1 u 2 -1 b c 2 j -1 v u -1 2 i w -1 n -1 l 0 n 2 l -1 n -1 d -1 s u -1