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 Cosh

 http://functions.wolfram.com/01.20.21.4865.01

 Input Form

 Integrate[E^(b Sqrt[z] + d z + e) Sin[a Sqrt[z] + p z + q]^m Sinh[w Sqrt[z] + s z + t]^u Cosh[c Sqrt[z] + f z + g]^v, z] == (I^u 2^(-1 - m - u - v) E^(-(b^2/(4 d)) + e) Binomial[m, m/2] Binomial[u, u/2] Binomial[v, v/2] (2 d E^((b + 2 d Sqrt[z])^2/(4 d)) Sqrt[-((b + 2 d Sqrt[z])^2/d)] + b (b + 2 d Sqrt[z]) Gamma[1/2, -((b + 2 d Sqrt[z])^2/(4 d))]) (1 - Mod[m, 2]) (1 - Mod[u, 2]) (1 - Mod[v, 2]))/(d^2 Sqrt[-((b + 2 d Sqrt[z])^2/d)]) + I^u 2^(-1 - m - u - v) Binomial[u, u/2] Binomial[v, v/2] (1 - Mod[u, 2]) (1 - Mod[v, 2]) Sum[(-1)^k Binomial[m, k] ((E^(e - (b + I a (2 k - m))^2/(4 (d + I (2 k - m) p)) + (I m Pi)/2 + I (2 k - m) q) (2 E^((b + I a (2 k - m) + 2 (d + I (2 k - m) p) Sqrt[z])^2/(4 (d + I (2 k - m) p))) (d + I (2 k - m) p) Sqrt[-((b + I a (2 k - m) + 2 (d + I (2 k - m) p) Sqrt[z])^2/ (d + I (2 k - m) p))] + (b + I a (2 k - m)) (b + I a (2 k - m) + 2 (d + I (2 k - m) p) Sqrt[z]) Gamma[1/2, -((b + I a (2 k - m) + 2 (d + I (2 k - m) p) Sqrt[z])^2/ (4 (d + I (2 k - m) p)))]))/((d + I (2 k - m) p)^2 Sqrt[-((b + I a (2 k - m) + 2 (d + I (2 k - m) p) Sqrt[z])^2/ (d + I (2 k - m) p))]) + (E^(e - (b + I a (-2 k + m))^2/(4 (d + I (-2 k + m) p)) - (I m Pi)/2 + I (-2 k + m) q) (2 E^((b + I a (-2 k + m) + 2 (d + I (-2 k + m) p) Sqrt[z])^2/(4 (d + I (-2 k + m) p))) (d + I (-2 k + m) p) Sqrt[-((b + I a (-2 k + m) + 2 (d + I (-2 k + m) p) Sqrt[z])^2/ (d + I (-2 k + m) p))] + (b + I a (-2 k + m)) (b + I a (-2 k + m) + 2 (d + I (-2 k + m) p) Sqrt[z]) Gamma[1/2, -((b + I a (-2 k + m) + 2 (d + I (-2 k + m) p) Sqrt[z])^ 2/(4 (d + I (-2 k + m) p)))]))/((d + I (-2 k + m) p)^2 Sqrt[-((b + I a (-2 k + m) + 2 (d + I (-2 k + m) p) Sqrt[z])^2/ (d + I (-2 k + m) p))])), {k, 0, Floor[(1/2) (-1 + m)]}] + 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)^k Binomial[u, k] ((E^(e + t (2 k - u) + (I Pi u)/2 - (b + (2 k - u) w)^2/ (4 (d + s (2 k - u)))) (2 E^((b + (2 k - u) w + 2 (d + s (2 k - u)) Sqrt[z])^2/ (4 (d + s (2 k - u)))) (d + s (2 k - u)) Sqrt[-((b + (2 k - u) w + 2 (d + s (2 k - u)) Sqrt[z])^2/ (d + s (2 k - u)))] + (b + (2 k - u) w) (b + (2 k - u) w + 2 (d + s (2 k - u)) Sqrt[z]) Gamma[1/2, -((b + (2 k - u) w + 2 (d + s (2 k - u)) Sqrt[z])^2/ (4 (d + s (2 k - u))))]))/((d + s (2 k - u))^2 Sqrt[-((b + (2 k - u) w + 2 (d + s (2 k - u)) Sqrt[z])^2/ (d + s (2 k - u)))]) + (E^(e - (I Pi u)/2 + t (-2 k + u) - (b + (-2 k + u) w)^2/ (4 (d + s (-2 k + u)))) (2 E^((b + (-2 k + u) w + 2 (d + s (-2 k + u)) Sqrt[z])^2/ (4 (d + s (-2 k + u)))) (d + s (-2 k + u)) Sqrt[-((b + (-2 k + u) w + 2 (d + s (-2 k + u)) Sqrt[z])^2/ (d + s (-2 k + u)))] + (b + (-2 k + u) w) (b + (-2 k + u) w + 2 (d + s (-2 k + u)) Sqrt[z]) Gamma[1/2, -((b + (-2 k + u) w + 2 (d + s (-2 k + u)) Sqrt[z])^2/ (4 (d + s (-2 k + u))))]))/((d + s (-2 k + u))^2 Sqrt[-((b + (-2 k + u) w + 2 (d + s (-2 k + u)) Sqrt[z])^2/ (d + s (-2 k + u)))])), {k, 0, Floor[(1/2) (-1 + u)]}] + 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, h] ((E^(e - (b + c (2 h - v))^2/(4 (d + f (2 h - v))) + g (2 h - v)) (2 E^((b + c (2 h - v) + 2 (d + f (2 h - v)) Sqrt[z])^2/ (4 (d + f (2 h - v)))) (d + f (2 h - v)) Sqrt[-((b + c (2 h - v) + 2 (d + f (2 h - v)) Sqrt[z])^2/ (d + f (2 h - v)))] + (b + c (2 h - v)) (b + c (2 h - v) + 2 (d + f (2 h - v)) Sqrt[z]) Gamma[1/2, -((b + c (2 h - v) + 2 (d + f (2 h - v)) Sqrt[z])^2/ (4 (d + f (2 h - v))))]))/((d + f (2 h - v))^2 Sqrt[-((b + c (2 h - v) + 2 (d + f (2 h - v)) Sqrt[z])^2/ (d + f (2 h - v)))]) + (E^(e - g (2 h - v) - (b + c (-2 h + v))^2/(4 (d + f (-2 h + v)))) (2 E^((b + c (-2 h + v) + 2 (d + f (-2 h + v)) Sqrt[z])^2/ (4 (d + f (-2 h + v)))) (d + f (-2 h + v)) Sqrt[-((b + c (-2 h + v) + 2 (d + f (-2 h + v)) Sqrt[z])^2/ (d + f (-2 h + v)))] + (b + c (-2 h + v)) (b + c (-2 h + v) + 2 (d + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((b + c (-2 h + v) + 2 (d + f (-2 h + v)) Sqrt[z])^2/ (4 (d + f (-2 h + v))))]))/((d + f (-2 h + v))^2 Sqrt[-((b + c (-2 h + v) + 2 (d + f (-2 h + v)) Sqrt[z])^2/ (d + f (-2 h + v)))])), {h, 0, Floor[(1/2) (-1 + v)]}] + I^u 2^(-1 - m - u - v) Binomial[v, v/2] (1 - Mod[v, 2]) Sum[(-1)^k Binomial[m, k] Sum[(-1)^j Binomial[u, j] ((E^(e + I (2 k - m) q + t (2 j - u) + (1/2) I Pi (m + u) - (b + I a (2 k - m) + (2 j - u) w)^2/(4 (d + I (2 k - m) p + s (2 j - u)))) (2 E^((b + I a (2 k - m) + (2 j - u) w + 2 (d + I (2 k - m) p + s (2 j - u)) Sqrt[z])^2/(4 (d + I (2 k - m) p + s (2 j - u)))) (d + I (2 k - m) p + s (2 j - u)) Sqrt[-((b + I a (2 k - m) + (2 j - u) w + 2 (d + I (2 k - m) p + s (2 j - u)) Sqrt[z])^2/ (d + I (2 k - m) p + s (2 j - u)))] + (b + I a (2 k - m) + (2 j - u) w) (b + I a (2 k - m) + (2 j - u) w + 2 (d + I (2 k - m) p + s (2 j - u)) Sqrt[z]) Gamma[1/2, -((b + I a (2 k - m) + (2 j - u) w + 2 (d + I (2 k - m) p + s (2 j - u)) Sqrt[z])^2/ (4 (d + I (2 k - m) p + s (2 j - u))))]))/ ((d + I (2 k - m) p + s (2 j - u))^2 Sqrt[-((b + I a (2 k - m) + (2 j - u) w + 2 (d + I (2 k - m) p + s (2 j - u)) Sqrt[z])^2/(d + I (2 k - m) p + s (2 j - u)))]) + (E^(e + I (-2 k + m) q + t (2 j - u) + (1/2) I Pi (-m + u) - (b + I a (-2 k + m) + (2 j - u) w)^2/ (4 (d + I (-2 k + m) p + s (2 j - u)))) (2 E^((b + I a (-2 k + m) + (2 j - u) w + 2 (d + I (-2 k + m) p + s (2 j - u)) Sqrt[z])^2/(4 (d + I (-2 k + m) p + s (2 j - u)))) (d + I (-2 k + m) p + s (2 j - u)) Sqrt[-((b + I a (-2 k + m) + (2 j - u) w + 2 (d + I (-2 k + m) p + s (2 j - u)) Sqrt[z])^2/(d + I (-2 k + m) p + s (2 j - u)))] + (b + I a (-2 k + m) + (2 j - u) w) (b + I a (-2 k + m) + (2 j - u) w + 2 (d + I (-2 k + m) p + s (2 j - u)) Sqrt[z]) Gamma[1/2, -((b + I a (-2 k + m) + (2 j - u) w + 2 (d + I (-2 k + m) p + s (2 j - u)) Sqrt[z])^ 2/(4 (d + I (-2 k + m) p + s (2 j - u))))]))/ ((d + I (-2 k + m) p + s (2 j - u))^2 Sqrt[-((b + I a (-2 k + m) + (2 j - u) w + 2 (d + I (-2 k + m) p + s (2 j - u)) Sqrt[z])^2/(d + I (-2 k + m) p + s (2 j - u)))]) + (E^(e + I (2 k - m) q + (1/2) I Pi (m - u) + t (-2 j + u) - (b + I a (2 k - m) + (-2 j + u) w)^2/ (4 (d + I (2 k - m) p + s (-2 j + u)))) (2 E^((b + I a (2 k - m) + (-2 j + u) w + 2 (d + I (2 k - m) p + s (-2 j + u)) Sqrt[z])^2/(4 (d + I (2 k - m) p + s (-2 j + u)))) (d + I (2 k - m) p + s (-2 j + u)) Sqrt[-((b + I a (2 k - m) + (-2 j + u) w + 2 (d + I (2 k - m) p + s (-2 j + u)) Sqrt[z])^2/(d + I (2 k - m) p + s (-2 j + u)))] + (b + I a (2 k - m) + (-2 j + u) w) (b + I a (2 k - m) + (-2 j + u) w + 2 (d + I (2 k - m) p + s (-2 j + u)) Sqrt[z]) Gamma[1/2, -((b + I a (2 k - m) + (-2 j + u) w + 2 (d + I (2 k - m) p + s (-2 j + u)) Sqrt[z])^2/(4 (d + I (2 k - m) p + s (-2 j + u))))]))/ ((d + I (2 k - m) p + s (-2 j + u))^2 Sqrt[-((b + I a (2 k - m) + (-2 j + u) w + 2 (d + I (2 k - m) p + s (-2 j + u)) Sqrt[z])^2/(d + I (2 k - m) p + s (-2 j + u)))]) + (E^(e + I (-2 k + m) q + t (-2 j + u) - (1/2) I Pi (m + u) - (b + I a (-2 k + m) + (-2 j + u) w)^2/ (4 (d + I (-2 k + m) p + s (-2 j + u)))) (2 E^((b + I a (-2 k + m) + (-2 j + u) w + 2 (d + I (-2 k + m) p + s (-2 j + u)) Sqrt[z])^2/(4 (d + I (-2 k + m) p + s (-2 j + u)))) (d + I (-2 k + m) p + s (-2 j + u)) Sqrt[-((b + I a (-2 k + m) + (-2 j + u) w + 2 (d + I (-2 k + m) p + s (-2 j + u)) Sqrt[z])^2/(d + I (-2 k + m) p + s (-2 j + u)))] + (b + I a (-2 k + m) + (-2 j + u) w) (b + I a (-2 k + m) + (-2 j + u) w + 2 (d + I (-2 k + m) p + s (-2 j + u)) Sqrt[z]) Gamma[1/2, -((b + I a (-2 k + m) + (-2 j + u) w + 2 (d + I (-2 k + m) p + s (-2 j + u)) Sqrt[z])^2/(4 (d + I (-2 k + m) p + s (-2 j + u))))]))/ ((d + I (-2 k + m) p + s (-2 j + u))^2 Sqrt[-((b + I a (-2 k + m) + (-2 j + u) w + 2 (d + I (-2 k + m) p + s (-2 j + u)) Sqrt[z])^2/(d + I (-2 k + m) p + s (-2 j + u)))])), {j, 0, Floor[(1/2) (-1 + u)]}], {k, 0, Floor[(1/2) (-1 + m)]}] + I^u 2^(-1 - m - u - v) Binomial[u, u/2] (1 - Mod[u, 2]) Sum[(-1)^k Binomial[m, k] Sum[Binomial[v, h] ((E^(e + (I m Pi)/2 + I (2 k - m) q - (b + I a (2 k - m) + c (2 h - v))^2/(4 (d + I (2 k - m) p + f (2 h - v))) + g (2 h - v)) (2 E^((b + I a (2 k - m) + c (2 h - v) + 2 (d + I (2 k - m) p + f (2 h - v)) Sqrt[z])^2/(4 (d + I (2 k - m) p + f (2 h - v)))) (d + I (2 k - m) p + f (2 h - v)) Sqrt[-((b + I a (2 k - m) + c (2 h - v) + 2 (d + I (2 k - m) p + f (2 h - v)) Sqrt[z])^2/(d + I (2 k - m) p + f (2 h - v)))] + (b + I a (2 k - m) + c (2 h - v)) (b + I a (2 k - m) + c (2 h - v) + 2 (d + I (2 k - m) p + f (2 h - v)) Sqrt[z]) Gamma[1/2, -((b + I a (2 k - m) + c (2 h - v) + 2 (d + I (2 k - m) p + f (2 h - v)) Sqrt[z])^ 2/(4 (d + I (2 k - m) p + f (2 h - v))))]))/ ((d + I (2 k - m) p + f (2 h - v))^2 Sqrt[-((b + I a (2 k - m) + c (2 h - v) + 2 (d + I (2 k - m) p + f (2 h - v)) Sqrt[z])^2/(d + I (2 k - m) p + f (2 h - v)))]) + (E^(e - (I m Pi)/2 + I (-2 k + m) q - (b + I a (-2 k + m) + c (2 h - v))^2/(4 (d + I (-2 k + m) p + f (2 h - v))) + g (2 h - v)) (2 E^((b + I a (-2 k + m) + c (2 h - v) + 2 (d + I (-2 k + m) p + f (2 h - v)) Sqrt[z])^2/(4 (d + I (-2 k + m) p + f (2 h - v)))) (d + I (-2 k + m) p + f (2 h - v)) Sqrt[-((b + I a (-2 k + m) + c (2 h - v) + 2 (d + I (-2 k + m) p + f (2 h - v)) Sqrt[z])^2/(d + I (-2 k + m) p + f (2 h - v)))] + (b + I a (-2 k + m) + c (2 h - v)) (b + I a (-2 k + m) + c (2 h - v) + 2 (d + I (-2 k + m) p + f (2 h - v)) Sqrt[z]) Gamma[1/2, -((b + I a (-2 k + m) + c (2 h - v) + 2 (d + I (-2 k + m) p + f (2 h - v)) Sqrt[z])^ 2/(4 (d + I (-2 k + m) p + f (2 h - v))))]))/ ((d + I (-2 k + m) p + f (2 h - v))^2 Sqrt[-((b + I a (-2 k + m) + c (2 h - v) + 2 (d + I (-2 k + m) p + f (2 h - v)) Sqrt[z])^2/(d + I (-2 k + m) p + f (2 h - v)))]) + (E^(e + (I m Pi)/2 + I (2 k - m) q + g (-2 h + v) - (b + I a (2 k - m) + c (-2 h + v))^2/ (4 (d + I (2 k - m) p + f (-2 h + v)))) (2 E^((b + I a (2 k - m) + c (-2 h + v) + 2 (d + I (2 k - m) p + f (-2 h + v)) Sqrt[z])^2/(4 (d + I (2 k - m) p + f (-2 h + v)))) (d + I (2 k - m) p + f (-2 h + v)) Sqrt[-((b + I a (2 k - m) + c (-2 h + v) + 2 (d + I (2 k - m) p + f (-2 h + v)) Sqrt[z])^2/(d + I (2 k - m) p + f (-2 h + v)))] + (b + I a (2 k - m) + c (-2 h + v)) (b + I a (2 k - m) + c (-2 h + v) + 2 (d + I (2 k - m) p + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((b + I a (2 k - m) + c (-2 h + v) + 2 (d + I (2 k - m) p + f (-2 h + v)) Sqrt[z])^2/(4 (d + I (2 k - m) p + f (-2 h + v))))]))/ ((d + I (2 k - m) p + f (-2 h + v))^2 Sqrt[-((b + I a (2 k - m) + c (-2 h + v) + 2 (d + I (2 k - m) p + f (-2 h + v)) Sqrt[z])^2/(d + I (2 k - m) p + f (-2 h + v)))]) + (E^(e - (I m Pi)/2 + I (-2 k + m) q + g (-2 h + v) - (b + I a (-2 k + m) + c (-2 h + v))^2/ (4 (d + I (-2 k + m) p + f (-2 h + v)))) (2 E^((b + I a (-2 k + m) + c (-2 h + v) + 2 (d + I (-2 k + m) p + f (-2 h + v)) Sqrt[z])^2/(4 (d + I (-2 k + m) p + f (-2 h + v)))) (d + I (-2 k + m) p + f (-2 h + v)) Sqrt[-((b + I a (-2 k + m) + c (-2 h + v) + 2 (d + I (-2 k + m) p + f (-2 h + v)) Sqrt[z])^2/(d + I (-2 k + m) p + f (-2 h + v)))] + (b + I a (-2 k + m) + c (-2 h + v)) (b + I a (-2 k + m) + c (-2 h + v) + 2 (d + I (-2 k + m) p + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((b + I a (-2 k + m) + c (-2 h + v) + 2 (d + I (-2 k + m) p + f (-2 h + v)) Sqrt[z])^2/(4 (d + I (-2 k + m) p + f (-2 h + v))))]))/ ((d + I (-2 k + m) p + f (-2 h + v))^2 Sqrt[-((b + I a (-2 k + m) + c (-2 h + v) + 2 (d + I (-2 k + m) p + f (-2 h + v)) Sqrt[z])^2/(d + I (-2 k + m) p + f (-2 h + v)))])), {h, 0, Floor[(1/2) (-1 + v)]}], {k, 0, Floor[(1/2) (-1 + m)]}] + I^u 2^(-1 - m - u - v) Binomial[m, m/2] (1 - Mod[m, 2]) Sum[(-1)^k Binomial[u, k] Sum[Binomial[v, h] ((E^(e + t (2 k - u) + (I Pi u)/2 + g (2 h - v) - (b + c (2 h - v) + (2 k - u) w)^2/(4 (d + s (2 k - u) + f (2 h - v)))) (2 E^((b + c (2 h - v) + (2 k - u) w + 2 (d + s (2 k - u) + f (2 h - v)) Sqrt[z])^2/(4 (d + s (2 k - u) + f (2 h - v)))) (d + s (2 k - u) + f (2 h - v)) Sqrt[-((b + c (2 h - v) + (2 k - u) w + 2 (d + s (2 k - u) + f (2 h - v)) Sqrt[z])^2/ (d + s (2 k - u) + f (2 h - v)))] + (b + c (2 h - v) + (2 k - u) w) (b + c (2 h - v) + (2 k - u) w + 2 (d + s (2 k - u) + f (2 h - v)) Sqrt[z]) Gamma[1/2, -((b + c (2 h - v) + (2 k - u) w + 2 (d + s (2 k - u) + f (2 h - v)) Sqrt[z])^2/(4 (d + s (2 k - u) + f (2 h - v))))]))/((d + s (2 k - u) + f (2 h - v))^2 Sqrt[-((b + c (2 h - v) + (2 k - u) w + 2 (d + s (2 k - u) + f (2 h - v)) Sqrt[z])^2/(d + s (2 k - u) + f (2 h - v)))]) + (E^(e - (I Pi u)/2 + t (-2 k + u) + g (2 h - v) - (b + c (2 h - v) + (-2 k + u) w)^2/ (4 (d + s (-2 k + u) + f (2 h - v)))) (2 E^((b + c (2 h - v) + (-2 k + u) w + 2 (d + s (-2 k + u) + f (2 h - v)) Sqrt[z])^2/(4 (d + s (-2 k + u) + f (2 h - v)))) (d + s (-2 k + u) + f (2 h - v)) Sqrt[-((b + c (2 h - v) + (-2 k + u) w + 2 (d + s (-2 k + u) + f (2 h - v)) Sqrt[z])^2/(d + s (-2 k + u) + f (2 h - v)))] + (b + c (2 h - v) + (-2 k + u) w) (b + c (2 h - v) + (-2 k + u) w + 2 (d + s (-2 k + u) + f (2 h - v)) Sqrt[z]) Gamma[1/2, -((b + c (2 h - v) + (-2 k + u) w + 2 (d + s (-2 k + u) + f (2 h - v)) Sqrt[z])^ 2/(4 (d + s (-2 k + u) + f (2 h - v))))]))/ ((d + s (-2 k + u) + f (2 h - v))^2 Sqrt[-((b + c (2 h - v) + (-2 k + u) w + 2 (d + s (-2 k + u) + f (2 h - v)) Sqrt[z])^2/(d + s (-2 k + u) + f (2 h - v)))]) + (E^(e + t (2 k - u) + (I Pi u)/2 + g (-2 h + v) - (b + c (-2 h + v) + (2 k - u) w)^2/ (4 (d + s (2 k - u) + f (-2 h + v)))) (2 E^((b + c (-2 h + v) + (2 k - u) w + 2 (d + s (2 k - u) + f (-2 h + v)) Sqrt[z])^2/(4 (d + s (2 k - u) + f (-2 h + v)))) (d + s (2 k - u) + f (-2 h + v)) Sqrt[-((b + c (-2 h + v) + (2 k - u) w + 2 (d + s (2 k - u) + f (-2 h + v)) Sqrt[z])^2/(d + s (2 k - u) + f (-2 h + v)))] + (b + c (-2 h + v) + (2 k - u) w) (b + c (-2 h + v) + (2 k - u) w + 2 (d + s (2 k - u) + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((b + c (-2 h + v) + (2 k - u) w + 2 (d + s (2 k - u) + f (-2 h + v)) Sqrt[z])^2/ (4 (d + s (2 k - u) + f (-2 h + v))))]))/ ((d + s (2 k - u) + f (-2 h + v))^2 Sqrt[-((b + c (-2 h + v) + (2 k - u) w + 2 (d + s (2 k - u) + f (-2 h + v)) Sqrt[z])^2/(d + s (2 k - u) + f (-2 h + v)))]) + (E^(e - (I Pi u)/2 + t (-2 k + u) + g (-2 h + v) - (b + c (-2 h + v) + (-2 k + u) w)^2/ (4 (d + s (-2 k + u) + f (-2 h + v)))) (2 E^((b + c (-2 h + v) + (-2 k + u) w + 2 (d + s (-2 k + u) + f (-2 h + v)) Sqrt[z])^2/(4 (d + s (-2 k + u) + f (-2 h + v)))) (d + s (-2 k + u) + f (-2 h + v)) Sqrt[-((b + c (-2 h + v) + (-2 k + u) w + 2 (d + s (-2 k + u) + f (-2 h + v)) Sqrt[z])^2/(d + s (-2 k + u) + f (-2 h + v)))] + (b + c (-2 h + v) + (-2 k + u) w) (b + c (-2 h + v) + (-2 k + u) w + 2 (d + s (-2 k + u) + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((b + c (-2 h + v) + (-2 k + u) w + 2 (d + s (-2 k + u) + f (-2 h + v)) Sqrt[z])^ 2/(4 (d + s (-2 k + u) + f (-2 h + v))))]))/ ((d + s (-2 k + u) + f (-2 h + v))^2 Sqrt[-((b + c (-2 h + v) + (-2 k + u) w + 2 (d + s (-2 k + u) + f (-2 h + v)) Sqrt[z])^2/(d + s (-2 k + u) + f (-2 h + v)))])), {h, 0, Floor[(1/2) (-1 + v)]}], {k, 0, Floor[(1/2) (-1 + u)]}] + I^u 2^(-1 - m - u - v) Sum[Binomial[v, h] Sum[(-1)^k Binomial[m, k] Sum[(-1)^j Binomial[u, j] ((E^(e + (I m Pi)/2 + I (2 k - m) q + t (2 j - u) + (I Pi u)/2 + g (2 h - v) - (b + I a (2 k - m) + c (2 h - v) + (2 j - u) w)^2/(4 (d + I (2 k - m) p + s (2 j - u) + f (2 h - v)))) (2 E^((b + I a (2 k - m) + c (2 h - v) + (2 j - u) w + 2 (d + I (2 k - m) p + s (2 j - u) + f (2 h - v)) Sqrt[z])^ 2/(4 (d + I (2 k - m) p + s (2 j - u) + f (2 h - v)))) (d + I (2 k - m) p + s (2 j - u) + f (2 h - v)) Sqrt[ -((b + I a (2 k - m) + c (2 h - v) + (2 j - u) w + 2 (d + I (2 k - m) p + s (2 j - u) + f (2 h - v)) Sqrt[z])^2/(d + I (2 k - m) p + s (2 j - u) + f (2 h - v)))] + (b + I a (2 k - m) + c (2 h - v) + (2 j - u) w) (b + I a (2 k - m) + c (2 h - v) + (2 j - u) w + 2 (d + I (2 k - m) p + s (2 j - u) + f (2 h - v)) Sqrt[z]) Gamma[1/2, -((b + I a (2 k - m) + c (2 h - v) + (2 j - u) w + 2 (d + I (2 k - m) p + s (2 j - u) + f (2 h - v)) Sqrt[z])^2/(4 (d + I (2 k - m) p + s (2 j - u) + f (2 h - v))))]))/((d + I (2 k - m) p + s (2 j - u) + f (2 h - v))^2 Sqrt[-((b + I a (2 k - m) + c (2 h - v) + (2 j - u) w + 2 (d + I (2 k - m) p + s (2 j - u) + f (2 h - v)) Sqrt[z])^2/(d + I (2 k - m) p + s (2 j - u) + f (2 h - v)))]) + (E^(e - (I m Pi)/2 + I (-2 k + m) q + t (2 j - u) + (I Pi u)/2 + g (2 h - v) - (b + I a (-2 k + m) + c (2 h - v) + (2 j - u) w)^ 2/(4 (d + I (-2 k + m) p + s (2 j - u) + f (2 h - v)))) (2 E^((b + I a (-2 k + m) + c (2 h - v) + (2 j - u) w + 2 (d + I (-2 k + m) p + s (2 j - u) + f (2 h - v)) Sqrt[z])^2/(4 (d + I (-2 k + m) p + s (2 j - u) + f (2 h - v)))) (d + I (-2 k + m) p + s (2 j - u) + f (2 h - v)) Sqrt[-((b + I a (-2 k + m) + c (2 h - v) + (2 j - u) w + 2 (d + I (-2 k + m) p + s (2 j - u) + f (2 h - v)) Sqrt[z])^2/(d + I (-2 k + m) p + s (2 j - u) + f (2 h - v)))] + (b + I a (-2 k + m) + c (2 h - v) + (2 j - u) w) (b + I a (-2 k + m) + c (2 h - v) + (2 j - u) w + 2 (d + I (-2 k + m) p + s (2 j - u) + f (2 h - v)) Sqrt[z]) Gamma[1/2, -((b + I a (-2 k + m) + c (2 h - v) + (2 j - u) w + 2 (d + I (-2 k + m) p + s (2 j - u) + f (2 h - v)) Sqrt[z])^2/(4 (d + I (-2 k + m) p + s (2 j - u) + f (2 h - v))))]))/((d + I (-2 k + m) p + s (2 j - u) + f (2 h - v))^2 Sqrt[-((b + I a (-2 k + m) + c (2 h - v) + (2 j - u) w + 2 (d + I (-2 k + m) p + s (2 j - u) + f (2 h - v)) Sqrt[z])^2/(d + I (-2 k + m) p + s (2 j - u) + f (2 h - v)))]) + (E^(e + (I m Pi)/2 + I (2 k - m) q - (I Pi u)/2 + t (-2 j + u) + g (2 h - v) - (b + I a (2 k - m) + c (2 h - v) + (-2 j + u) w)^ 2/(4 (d + I (2 k - m) p + s (-2 j + u) + f (2 h - v)))) (2 E^((b + I a (2 k - m) + c (2 h - v) + (-2 j + u) w + 2 (d + I (2 k - m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z])^2/(4 (d + I (2 k - m) p + s (-2 j + u) + f (2 h - v)))) (d + I (2 k - m) p + s (-2 j + u) + f (2 h - v)) Sqrt[-((b + I a (2 k - m) + c (2 h - v) + (-2 j + u) w + 2 (d + I (2 k - m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z])^2/(d + I (2 k - m) p + s (-2 j + u) + f (2 h - v)))] + (b + I a (2 k - m) + c (2 h - v) + (-2 j + u) w) (b + I a (2 k - m) + c (2 h - v) + (-2 j + u) w + 2 (d + I (2 k - m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z]) Gamma[1/2, -((b + I a (2 k - m) + c (2 h - v) + (-2 j + u) w + 2 (d + I (2 k - m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z])^2/(4 (d + I (2 k - m) p + s (-2 j + u) + f (2 h - v))))]))/((d + I (2 k - m) p + s (-2 j + u) + f (2 h - v))^2 Sqrt[-((b + I a (2 k - m) + c (2 h - v) + (-2 j + u) w + 2 (d + I (2 k - m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z])^2/(d + I (2 k - m) p + s (-2 j + u) + f (2 h - v)))]) + (E^(e - (I m Pi)/2 + I (-2 k + m) q - (I Pi u)/2 + t (-2 j + u) + g (2 h - v) - (b + I a (-2 k + m) + c (2 h - v) + (-2 j + u) w)^2/(4 (d + I (-2 k + m) p + s (-2 j + u) + f (2 h - v)))) (2 E^((b + I a (-2 k + m) + c (2 h - v) + (-2 j + u) w + 2 (d + I (-2 k + m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z])^2/(4 (d + I (-2 k + m) p + s (-2 j + u) + f (2 h - v)))) (d + I (-2 k + m) p + s (-2 j + u) + f (2 h - v)) Sqrt[-((b + I a (-2 k + m) + c (2 h - v) + (-2 j + u) w + 2 (d + I (-2 k + m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z])^2/(d + I (-2 k + m) p + s (-2 j + u) + f (2 h - v)))] + (b + I a (-2 k + m) + c (2 h - v) + (-2 j + u) w) (b + I a (-2 k + m) + c (2 h - v) + (-2 j + u) w + 2 (d + I (-2 k + m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z]) Gamma[1/2, -((b + I a (-2 k + m) + c (2 h - v) + (-2 j + u) w + 2 (d + I (-2 k + m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z])^2/(4 (d + I (-2 k + m) p + s (-2 j + u) + f (2 h - v))))]))/((d + I (-2 k + m) p + s (-2 j + u) + f (2 h - v))^2 Sqrt[-((b + I a (-2 k + m) + c (2 h - v) + (-2 j + u) w + 2 (d + I (-2 k + m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z])^2/(d + I (-2 k + m) p + s (-2 j + u) + f (2 h - v)))]) + (E^(e + (I m Pi)/2 + I (2 k - m) q + t (2 j - u) + (I Pi u)/2 + g (-2 h + v) - (b + I a (2 k - m) + c (-2 h + v) + (2 j - u) w)^ 2/(4 (d + I (2 k - m) p + s (2 j - u) + f (-2 h + v)))) (2 E^((b + I a (2 k - m) + c (-2 h + v) + (2 j - u) w + 2 (d + I (2 k - m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z])^2/(4 (d + I (2 k - m) p + s (2 j - u) + f (-2 h + v)))) (d + I (2 k - m) p + s (2 j - u) + f (-2 h + v)) Sqrt[-((b + I a (2 k - m) + c (-2 h + v) + (2 j - u) w + 2 (d + I (2 k - m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z])^2/(d + I (2 k - m) p + s (2 j - u) + f (-2 h + v)))] + (b + I a (2 k - m) + c (-2 h + v) + (2 j - u) w) (b + I a (2 k - m) + c (-2 h + v) + (2 j - u) w + 2 (d + I (2 k - m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((b + I a (2 k - m) + c (-2 h + v) + (2 j - u) w + 2 (d + I (2 k - m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z])^2/(4 (d + I (2 k - m) p + s (2 j - u) + f (-2 h + v))))]))/((d + I (2 k - m) p + s (2 j - u) + f (-2 h + v))^2 Sqrt[-((b + I a (2 k - m) + c (-2 h + v) + (2 j - u) w + 2 (d + I (2 k - m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z])^2/(d + I (2 k - m) p + s (2 j - u) + f (-2 h + v)))]) + (E^(e - (I m Pi)/2 + I (-2 k + m) q + t (2 j - u) + (I Pi u)/2 + g (-2 h + v) - (b + I a (-2 k + m) + c (-2 h + v) + (2 j - u) w)^2/(4 (d + I (-2 k + m) p + s (2 j - u) + f (-2 h + v)))) (2 E^((b + I a (-2 k + m) + c (-2 h + v) + (2 j - u) w + 2 (d + I (-2 k + m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z])^2/(4 (d + I (-2 k + m) p + s (2 j - u) + f (-2 h + v)))) (d + I (-2 k + m) p + s (2 j - u) + f (-2 h + v)) Sqrt[-((b + I a (-2 k + m) + c (-2 h + v) + (2 j - u) w + 2 (d + I (-2 k + m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z])^2/(d + I (-2 k + m) p + s (2 j - u) + f (-2 h + v)))] + (b + I a (-2 k + m) + c (-2 h + v) + (2 j - u) w) (b + I a (-2 k + m) + c (-2 h + v) + (2 j - u) w + 2 (d + I (-2 k + m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((b + I a (-2 k + m) + c (-2 h + v) + (2 j - u) w + 2 (d + I (-2 k + m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z])^2/(4 (d + I (-2 k + m) p + s (2 j - u) + f (-2 h + v))))]))/((d + I (-2 k + m) p + s (2 j - u) + f (-2 h + v))^2 Sqrt[-((b + I a (-2 k + m) + c (-2 h + v) + (2 j - u) w + 2 (d + I (-2 k + m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z])^2/(d + I (-2 k + m) p + s (2 j - u) + f (-2 h + v)))]) + (E^(e + (I m Pi)/2 + I (2 k - m) q - (I Pi u)/2 + t (-2 j + u) + g (-2 h + v) - (b + I a (2 k - m) + c (-2 h + v) + (-2 j + u) w)^2/(4 (d + I (2 k - m) p + s (-2 j + u) + f (-2 h + v)))) (2 E^((b + I a (2 k - m) + c (-2 h + v) + (-2 j + u) w + 2 (d + I (2 k - m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z])^2/(4 (d + I (2 k - m) p + s (-2 j + u) + f (-2 h + v)))) (d + I (2 k - m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[-((b + I a (2 k - m) + c (-2 h + v) + (-2 j + u) w + 2 (d + I (2 k - m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z])^2/ (d + I (2 k - m) p + s (-2 j + u) + f (-2 h + v)))] + (b + I a (2 k - m) + c (-2 h + v) + (-2 j + u) w) (b + I a (2 k - m) + c (-2 h + v) + (-2 j + u) w + 2 (d + I (2 k - m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((b + I a (2 k - m) + c (-2 h + v) + (-2 j + u) w + 2 (d + I (2 k - m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z])^2/(4 (d + I (2 k - m) p + s (-2 j + u) + f (-2 h + v))))]))/((d + I (2 k - m) p + s (-2 j + u) + f (-2 h + v))^2 Sqrt[-((b + I a (2 k - m) + c (-2 h + v) + (-2 j + u) w + 2 (d + I (2 k - m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z])^2/(d + I (2 k - m) p + s (-2 j + u) + f (-2 h + v)))]) + (E^(e - (I m Pi)/2 + I (-2 k + m) q - (I Pi u)/2 + t (-2 j + u) + g (-2 h + v) - (b + I a (-2 k + m) + c (-2 h + v) + (-2 j + u) w)^2/(4 (d + I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)))) (2 E^((b + I a (-2 k + m) + c (-2 h + v) + (-2 j + u) w + 2 (d + I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z])^2/(4 (d + I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)))) (d + I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[-((b + I a (-2 k + m) + c (-2 h + v) + (-2 j + u) w + 2 (d + I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z])^2/ (d + I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)))] + (b + I a (-2 k + m) + c (-2 h + v) + (-2 j + u) w) (b + I a (-2 k + m) + c (-2 h + v) + (-2 j + u) w + 2 (d + I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((b + I a (-2 k + m) + c (-2 h + v) + (-2 j + u) w + 2 (d + I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z])^2/(4 (d + I (-2 k + m) p + s (-2 j + u) + f (-2 h + v))))]))/((d + I (-2 k + m) p + s (-2 j + u) + f (-2 h + v))^2 Sqrt[-((b + I a (-2 k + m) + c (-2 h + v) + (-2 j + u) w + 2 (d + I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z])^2/(d + I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)))])), {j, 0, Floor[(1/2) (-1 + u)]}], {k, 0, Floor[(1/2) (-1 + m)]}], {h, 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

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