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/01.20.21.4931.01

 Input Form

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

 Standard Form

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 MathML Form

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