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/01.20.21.4870.01

 Input Form

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

 Standard Form

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 MathML Form

 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 - u 2 - m - u - v - 1 ( d + 2 b z ) ( 1 - m mod 2 \$CellContext`m 2 ) ( 1 - u mod 2 \$CellContext`u 2 ) ( 1 - v mod 2 \$CellContext`v 2 ) b - ( d + 2 b z ) 2 b e - d 2 4 b ( 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]]]]] Γ ( 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 ( d + ( 2 j - m ) p + 2 ( b + a ( 2 j - m ) ) z ) Γ ( 1 2 , - ( d + ( 2 j - m ) p + 2 ( b + a ( 2 j - m ) ) z ) 2 4 ( b + a ( 2 j - m ) ) ) ) / ( ( b + a ( 2 j - m ) ) - ( d + ( 2 j - m ) p + 2 ( b + a ( 2 j - m ) ) z ) 2 b + a ( 2 j - m ) ) + ( - ( d + ( m - 2 j ) p ) 2 4 ( b + a ( m - 2 j ) ) + e + ( m - 2 j ) q ( d + ( m - 2 j ) p + 2 ( b + a ( m - 2 j ) ) z ) Γ ( 1 2 , - ( d + ( m - 2 j ) p + 2 ( b + a ( m - 2 j ) ) z ) 2 4 ( b + a ( m - 2 j ) ) ) ) / ( ( b + a ( m - 2 j ) ) - ( d + ( m - 2 j ) p + 2 ( b + a ( m - 2 j ) ) z ) 2 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 ) ( d + f ( 2 j - v ) + 2 ( b + c ( 2 j - v ) ) z ) Γ ( 1 2 , - ( d + f ( 2 j - v ) + 2 ( b + c ( 2 j - v ) ) z ) 2 4 ( b + c ( 2 j - v ) ) ) ) / ( ( b + c ( 2 j - v ) ) - ( d + f ( 2 j - v ) + 2 ( b + c ( 2 j - v ) ) z ) 2 b + c ( 2 j - v ) ) + ( - ( d + f ( v - 2 j ) ) 2 4 ( b + c ( v - 2 j ) ) + e + g ( v - 2 j ) ( d + f ( v - 2 j ) + 2 ( b + c ( v - 2 j ) ) z ) Γ ( 1 2 , - ( d + f ( v - 2 j ) + 2 ( b + c ( v - 2 j ) ) z ) 2 4 ( b + c ( v - 2 j ) ) ) ) / ( ( b + c ( v - 2 j ) ) - ( d + f ( v - 2 j ) + 2 ( b + c ( v - 2 j ) ) z ) 2 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 ( d + s ( 2 i - u ) + 2 ( b + ( 2 i - u ) w ) z ) Γ ( 1 2 , - ( d + s ( 2 i - u ) + 2 ( b + ( 2 i - u ) w ) z ) 2 4 ( b + ( 2 i - u ) w ) ) ) / ( ( b + ( 2 i - u ) w ) - ( d + s ( 2 i - u ) + 2 ( b + ( 2 i - u ) w ) z ) 2 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 ( d + s ( u - 2 i ) + 2 ( b + ( u - 2 i ) w ) z ) Γ ( 1 2 , - ( d + s ( u - 2 i ) + 2 ( b + ( u - 2 i ) w ) z ) 2 4 ( b + ( u - 2 i ) w ) ) ) / ( ( b + ( u - 2 i ) w ) - ( d + s ( u - 2 i ) + 2 ( b + ( u - 2 i ) w ) z ) 2 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 ) ( d + ( 2 k - m ) p + f ( 2 j - v ) + 2 ( b + a ( 2 k - m ) + c ( 2 j - v ) ) z ) Γ ( 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 ) ) ) ) ) / ( ( b + a ( 2 k - m ) + c ( 2 j - v ) ) ( - ( 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 ) ) ) ) + ( - ( 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 ) ( d + ( m - 2 k ) p + f ( 2 j - v ) + 2 ( b + a ( m - 2 k ) + c ( 2 j - v ) ) z ) Γ ( 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 ) ) ) ) ) / ( ( b + a ( m - 2 k ) + c ( 2 j - v ) ) ( - ( 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 ) ) ) ) + ( - ( 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 ) ( d + ( 2 k - m ) p + f ( v - 2 j ) + 2 ( b + a ( 2 k - m ) + c ( v - 2 j ) ) z ) Γ ( 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 ) ) ) ) ) / ( ( b + a ( 2 k - m ) + c ( v - 2 j ) ) ( - ( 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 ) ) ) ) + ( - ( 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 ) ( d + ( m - 2 k ) p + f ( v - 2 j ) + 2 ( b + a ( m - 2 k ) + c ( v - 2 j ) ) z ) Γ ( 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 ) ) ) ) ) / ( ( b + a ( m - 2 k ) + c ( v - 2 j ) ) ( - ( 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 ) ) ) ) ) - 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 ( d + ( 2 j - m ) p + s ( 2 i - u ) + 2 ( b + a ( 2 j - m ) + ( 2 i - u ) w ) z ) Γ ( 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 ) ) ) ) / ( ( b + a ( 2 j - m ) + ( 2 i - u ) w ) ( - ( 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 ) ) ) + ( - ( 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 ( d + ( m - 2 j ) p + s ( 2 i - u ) + 2 ( b + a ( m - 2 j ) + ( 2 i - u ) w ) z ) Γ ( 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 ) ) ) ) / ( ( b + a ( m - 2 j ) + ( 2 i - u ) w ) ( - ( 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 ) ) ) + ( - ( 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 ( d + ( 2 j - m ) p + s ( u - 2 i ) + 2 ( b + a ( 2 j - m ) + ( u - 2 i ) w ) z ) Γ ( 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 ) ) ) ) / ( ( b + a ( 2 j - m ) + ( u - 2 i ) w ) ( - ( 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 ) ) ) + ( - ( 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 ( d + ( m - 2 j ) p + s ( u - 2 i ) + 2 ( b + a ( m - 2 j ) + ( u - 2 i ) w ) z ) Γ ( 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 ) ) ) ) / ( ( b + a ( m - 2 j ) + ( u - 2 i ) w ) ( - ( 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 ) ) ) ) - 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 ) ( d + s ( 2 i - u ) + f ( 2 j - v ) + 2 ( b + c ( 2 j - v ) + ( 2 i - u ) w ) z ) Γ ( 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 ) ) ) / ( ( b + c ( 2 j - v ) + ( 2 i - u ) w ) - ( 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 ) + ( - ( 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 ) ( d + s ( 2 i - u ) + f ( v - 2 j ) + 2 ( b + c ( v - 2 j ) + ( 2 i - u ) w ) z ) Γ ( 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 ) ) ) / ( ( b + c ( v - 2 j ) + ( 2 i - u ) w ) - ( 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 ) + ( - ( 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 ( d + s ( u - 2 i ) + f ( 2 j - v ) + 2 ( b + c ( 2 j - v ) + ( u - 2 i ) w ) z ) Γ ( 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 ) ) ) / ( ( b + c ( 2 j - v ) + ( u - 2 i ) w ) - ( 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 ) + ( - ( 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 ( d + s ( u - 2 i ) + f ( v - 2 j ) + 2 ( b + c ( v - 2 j ) + ( u - 2 i ) w ) z ) Γ ( 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 ) ) ) / ( ( b + c ( v - 2 j ) + ( u - 2 i ) w ) - ( 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 ) ) - 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 ) ( 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 ) Γ ( 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 ) ) ) ) / ( ( b + a ( 2 j - m ) + c ( 2 k - v ) + ( 2 i - u ) w ) ( - ( 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 ) ) ) + ( - ( 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 ) ( 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 ) Γ ( 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 ) ) ) ) / ( ( b + a ( m - 2 j ) + c ( 2 k - v ) + ( 2 i - u ) w ) ( - ( 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 ) ) ) + ( - ( 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 ) ( 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 ) Γ ( 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 ) ) ) ) / ( ( b + a ( 2 j - m ) + c ( v - 2 k ) + ( 2 i - u ) w ) ( - ( 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 ) ) ) + ( - ( 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 ) ( 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 ) Γ ( 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 ) ) ) ) / ( ( b + a ( m - 2 j ) + c ( v - 2 k ) + ( 2 i - u ) w ) ( - ( 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 ) ) ) + ( - ( 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 ( 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 ) Γ ( 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 ) ) ) ) / ( ( b + a ( 2 j - m ) + c ( 2 k - v ) + ( u - 2 i ) w ) ( - ( 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 ) ) ) + ( - ( 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 ( 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 ) Γ ( 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 ) ) ) ) / ( ( b + a ( m - 2 j ) + c ( 2 k - v ) + ( u - 2 i ) w ) ( - ( 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 ) ) ) + ( - ( 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 ( 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 ) Γ ( 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 ) ) ) ) / ( ( b + a ( 2 j - m ) + c ( v - 2 k ) + ( u - 2 i ) w ) ( - ( 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 ) ) ) + ( - ( 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 ( 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 ) Γ ( 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 ) ) ) ) / ( ( b + a ( m - 2 j ) + c ( v - 2 k ) + ( u - 2 i ) w ) ( - ( 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 ) ) ) ) /; m + u + v + Condition z 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 -1 u 2 -1 m -1 u -1 v -1 d 2 b z 1 -1 \$CellContext`m 2 1 -1 \$CellContext`u 2 1 -1 \$CellContext`v 2 b -1 d 2 b z 2 b -1 1 2 -1 e -1 d 2 4 b -1 Binomial m m 2 -1 Binomial u u 2 -1 Binomial v v 2 -1 Gamma 1 2 -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 d 2 j -1 m p 2 b a 2 j -1 m z Gamma 1 2 -1 d 2 j -1 m p 2 b a 2 j -1 m z 2 4 b a 2 j -1 m -1 b a 2 j -1 m -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 -1 d m -1 2 j p 2 4 b a m -1 2 j -1 e m -1 2 j q d m -1 2 j p 2 b a m -1 2 j z Gamma 1 2 -1 d m -1 2 j p 2 b a m -1 2 j z 2 4 b a m -1 2 j -1 b a m -1 2 j -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 -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 d f 2 j -1 v 2 b c 2 j -1 v z Gamma 1 2 -1 d f 2 j -1 v 2 b c 2 j -1 v z 2 4 b c 2 j -1 v -1 b c 2 j -1 v -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 -1 d f v -1 2 j 2 4 b c v -1 2 j -1 e g v -1 2 j d f v -1 2 j 2 b c v -1 2 j z Gamma 1 2 -1 d f v -1 2 j 2 b c v -1 2 j z 2 4 b c v -1 2 j -1 b c v -1 2 j -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 -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 d s 2 i -1 u 2 b 2 i -1 u w z Gamma 1 2 -1 d s 2 i -1 u 2 b 2 i -1 u w z 2 4 b 2 i -1 u w -1 b 2 i -1 u w -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 -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 d s u -1 2 i 2 b u -1 2 i w z Gamma 1 2 -1 d s u -1 2 i 2 b u -1 2 i w z 2 4 b u -1 2 i w -1 b u -1 2 i w -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 -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 d 2 k -1 m p f 2 j -1 v 2 b a 2 k -1 m c 2 j -1 v z Gamma 1 2 -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 b a 2 k -1 m c 2 j -1 v -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 -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 d m -1 2 k p f 2 j -1 v 2 b a m -1 2 k c 2 j -1 v z Gamma 1 2 -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 b a m -1 2 k c 2 j -1 v -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 -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 d 2 k -1 m p f v -1 2 j 2 b a 2 k -1 m c v -1 2 j z Gamma 1 2 -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 b a 2 k -1 m c v -1 2 j -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 -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 d m -1 2 k p f v -1 2 j 2 b a m -1 2 k c v -1 2 j z Gamma 1 2 -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 b a m -1 2 k c v -1 2 j -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 -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 d 2 j -1 m p s 2 i -1 u 2 b a 2 j -1 m 2 i -1 u w z Gamma 1 2 -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 b a 2 j -1 m 2 i -1 u w -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 -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 d m -1 2 j p s 2 i -1 u 2 b a m -1 2 j 2 i -1 u w z Gamma 1 2 -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 b a m -1 2 j 2 i -1 u w -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 -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 d 2 j -1 m p s u -1 2 i 2 b a 2 j -1 m u -1 2 i w z Gamma 1 2 -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 b a 2 j -1 m u -1 2 i w -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 -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 d m -1 2 j p s u -1 2 i 2 b a m -1 2 j u -1 2 i w z Gamma 1 2 -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 b a m -1 2 j u -1 2 i w -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 -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 d s 2 i -1 u f 2 j -1 v 2 b c 2 j -1 v 2 i -1 u w z Gamma 1 2 -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 b c 2 j -1 v 2 i -1 u w -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 -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 d s 2 i -1 u f v -1 2 j 2 b c v -1 2 j 2 i -1 u w z Gamma 1 2 -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 b c v -1 2 j 2 i -1 u w -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 -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 d s u -1 2 i f 2 j -1 v 2 b c 2 j -1 v u -1 2 i w z Gamma 1 2 -1 d s u -1 2 i f 2 j -1 v 2 b c 2 j -1 v u -1 2 i w z 2 4 b c 2 j -1 v u -1 2 i w -1 b c 2 j -1 v u -1 2 i w -1 d s u -1 2 i f 2 j -1 v 2 b c 2 j -1 v u -1 2 i w z 2 b c 2 j -1 v u -1 2 i w -1 1 2 -1 -1 d s u -1 2 i f v -1 2 j 2 4 b c v -1 2 j u -1 2 i w -1 e t u -1 2 i g v -1 2 j -1 u 2 -1 d s u -1 2 i f v -1 2 j 2 b c v -1 2 j u -1 2 i w z Gamma 1 2 -1 d s u -1 2 i f v -1 2 j 2 b c v -1 2 j u -1 2 i w z 2 4 b c v -1 2 j u -1 2 i w -1 b c v -1 2 j u -1 2 i w -1 d s u -1 2 i f v -1 2 j 2 b c v -1 2 j u -1 2 i w z 2 b c v -1 2 j u -1 2 i w -1 1 2 -1 -1 u 2 -1 m -1 u -1 v -1 k 0 v -1 2 -1 Binomial v k 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 f 2 k -1 v 2 4 b a 2 j -1 m c 2 k -1 v 2 i -1 u w -1 e 2 j -1 m q t 2 i -1 u u 2 -1 g 2 k -1 v d 2 j -1 m p s 2 i -1 u f 2 k -1 v 2 b a 2 j -1 m c 2 k -1 v 2 i -1 u w z Gamma 1 2 -1 d 2 j -1 m p s 2 i -1 u f 2 k -1 v 2 b a 2 j -1 m c 2 k -1 v 2 i -1 u w z 2 4 b a 2 j -1 m c 2 k -1 v 2 i -1 u w -1 b a 2 j -1 m c 2 k -1 v 2 i -1 u w -1 d 2 j -1 m p s 2 i -1 u f 2 k -1 v 2 b a 2 j -1 m c 2 k -1 v 2 i -1 u w z 2 b a 2 j -1 m c 2 k -1 v 2 i -1 u w -1 -1 -1 d m -1 2 j p s 2 i -1 u f 2 k -1 v 2 4 b a m -1 2 j c 2 k -1 v 2 i -1 u w -1 e m -1 2 j q t 2 i -1 u u 2 -1 g 2 k -1 v d m -1 2 j p s 2 i -1 u f 2 k -1 v 2 b a m -1 2 j c 2 k -1 v 2 i -1 u w z Gamma 1 2 -1 d m -1 2 j p s 2 i -1 u f 2 k -1 v 2 b a m -1 2 j c 2 k -1 v 2 i -1 u w z 2 4 b a m -1 2 j c 2 k -1 v 2 i -1 u w -1 b a m -1 2 j c 2 k -1 v 2 i -1 u w -1 d m -1 2 j p s 2 i -1 u f 2 k -1 v 2 b a m -1 2 j c 2 k -1 v 2 i -1 u w z 2 b a m -1 2 j c 2 k -1 v 2 i -1 u w -1 -1 -1 d 2 j -1 m p s 2 i -1 u f v -1 2 k 2 4 b a 2 j -1 m c v -1 2 k 2 i 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