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 Cosh

 http://functions.wolfram.com/01.20.21.4749.01

 Input Form

 Integrate[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^(-m - u - v) z Binomial[m, m/2] Binomial[u, u/2] Binomial[v, v/2] (1 - Mod[m, 2]) (1 - Mod[u, 2]) (1 - Mod[v, 2]) - I^u 2^(-1 - m - u - v) Binomial[u, u/2] Binomial[v, v/2] (1 - Mod[u, 2]) (1 - Mod[v, 2]) Sum[(-1)^k Binomial[m, k] ((E^(-((I a^2 (2 k - m))/(4 p)) + (I m Pi)/2 + I (2 k - m) q) ((2 I (2 k - m) p Sqrt[(I (I a (2 k - m) + 2 I (2 k - m) p Sqrt[z])^ 2)/((2 k - m) p)])/E^((I (I a (2 k - m) + 2 I (2 k - m) p Sqrt[z])^2)/(4 (2 k - m) p)) + I a (2 k - m) (I a (2 k - m) + 2 I (2 k - m) p Sqrt[z]) Gamma[1/2, (I (I a (2 k - m) + 2 I (2 k - m) p Sqrt[z])^2)/ (4 (2 k - m) p)]))/((2 k - m)^2 p^2 Sqrt[(I (I a (2 k - m) + 2 I (2 k - m) p Sqrt[z])^2)/ ((2 k - m) p)]) + (E^(-((I a^2 (-2 k + m))/(4 p)) - (I m Pi)/2 + I (-2 k + m) q) ((2 I (-2 k + m) p Sqrt[(I (I a (-2 k + m) + 2 I (-2 k + m) p Sqrt[z])^2)/ ((-2 k + m) p)])/E^((I (I a (-2 k + m) + 2 I (-2 k + m) p Sqrt[z])^2)/(4 (-2 k + m) p)) + I a (-2 k + m) (I a (-2 k + m) + 2 I (-2 k + m) p Sqrt[z]) Gamma[1/2, (I (I a (-2 k + m) + 2 I (-2 k + m) p Sqrt[z])^2)/ (4 (-2 k + m) p)]))/((-2 k + m)^2 p^2 Sqrt[(I (I a (-2 k + m) + 2 I (-2 k + m) p Sqrt[z])^2)/ ((-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^(t (2 k - u) + (I Pi u)/2 - ((2 k - u) w^2)/(4 s)) (2 E^(((2 k - u) w + 2 s (2 k - u) Sqrt[z])^2/(4 s (2 k - u))) s (2 k - u) Sqrt[-(((2 k - u) w + 2 s (2 k - u) Sqrt[z])^2/ (s (2 k - u)))] + (2 k - u) w ((2 k - u) w + 2 s (2 k - u) Sqrt[z]) Gamma[1/2, -(((2 k - u) w + 2 s (2 k - u) Sqrt[z])^2/(4 s (2 k - u)))]))/ (s^2 (2 k - u)^2 Sqrt[-(((2 k - u) w + 2 s (2 k - u) Sqrt[z])^2/ (s (2 k - u)))]) + (E^((-(1/2)) I Pi u + t (-2 k + u) - ((-2 k + u) w^2)/(4 s)) (2 E^(((-2 k + u) w + 2 s (-2 k + u) Sqrt[z])^2/(4 s (-2 k + u))) s (-2 k + u) Sqrt[-(((-2 k + u) w + 2 s (-2 k + u) Sqrt[z])^2/ (s (-2 k + u)))] + (-2 k + u) w ((-2 k + u) w + 2 s (-2 k + u) Sqrt[z]) Gamma[1/2, -(((-2 k + u) w + 2 s (-2 k + u) Sqrt[z])^2/(4 s (-2 k + u)))]))/ (s^2 (-2 k + u)^2 Sqrt[-(((-2 k + u) w + 2 s (-2 k + u) Sqrt[z])^2/ (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^(-((c^2 (2 h - v))/(4 f)) + g (2 h - v)) (2 E^((c (2 h - v) + 2 f (2 h - v) Sqrt[z])^2/(4 f (2 h - v))) f (2 h - v) Sqrt[-((c (2 h - v) + 2 f (2 h - v) Sqrt[z])^2/ (f (2 h - v)))] + c (2 h - v) (c (2 h - v) + 2 f (2 h - v) Sqrt[z]) Gamma[1/2, -((c (2 h - v) + 2 f (2 h - v) Sqrt[z])^2/(4 f (2 h - v)))]))/ (f^2 (2 h - v)^2 Sqrt[-((c (2 h - v) + 2 f (2 h - v) Sqrt[z])^2/ (f (2 h - v)))]) + (E^(-((c^2 (-2 h + v))/(4 f)) + g (-2 h + v)) (2 E^((c (-2 h + v) + 2 f (-2 h + v) Sqrt[z])^2/(4 f (-2 h + v))) f (-2 h + v) Sqrt[-((c (-2 h + v) + 2 f (-2 h + v) Sqrt[z])^2/ (f (-2 h + v)))] + c (-2 h + v) (c (-2 h + v) + 2 f (-2 h + v) Sqrt[z]) Gamma[1/2, -((c (-2 h + v) + 2 f (-2 h + v) Sqrt[z])^2/(4 f (-2 h + v)))]))/ (f^2 (-2 h + v)^2 Sqrt[-((c (-2 h + v) + 2 f (-2 h + v) Sqrt[z])^2/ (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^((I m Pi)/2 + I (2 k - m) q + t (2 j - u) + (I Pi u)/2 - (I a (2 k - m) + (2 j - u) w)^2/(4 (I (2 k - m) p + s (2 j - u)))) (2 E^((I a (2 k - m) + (2 j - u) w + 2 (I (2 k - m) p + s (2 j - u)) Sqrt[z])^2/(4 (I (2 k - m) p + s (2 j - u)))) (I (2 k - m) p + s (2 j - u)) Sqrt[-((I a (2 k - m) + (2 j - u) w + 2 (I (2 k - m) p + s (2 j - u)) Sqrt[z])^2/(I (2 k - m) p + s (2 j - u)))] + (I a (2 k - m) + (2 j - u) w) (I a (2 k - m) + (2 j - u) w + 2 (I (2 k - m) p + s (2 j - u)) Sqrt[z]) Gamma[1/2, -((I a (2 k - m) + (2 j - u) w + 2 (I (2 k - m) p + s (2 j - u)) Sqrt[z])^2/(4 (I (2 k - m) p + s (2 j - u))))]))/((I (2 k - m) p + s (2 j - u))^2 Sqrt[-((I a (2 k - m) + (2 j - u) w + 2 (I (2 k - m) p + s (2 j - u)) Sqrt[z])^2/(I (2 k - m) p + s (2 j - u)))]) + (E^((-(1/2)) I m Pi + I (-2 k + m) q + t (2 j - u) + (I Pi u)/2 - (I a (-2 k + m) + (2 j - u) w)^2/(4 (I (-2 k + m) p + s (2 j - u)))) (2 E^((I a (-2 k + m) + (2 j - u) w + 2 (I (-2 k + m) p + s (2 j - u)) Sqrt[z])^2/(4 (I (-2 k + m) p + s (2 j - u)))) (I (-2 k + m) p + s (2 j - u)) Sqrt[-((I a (-2 k + m) + (2 j - u) w + 2 (I (-2 k + m) p + s (2 j - u)) Sqrt[z])^2/ (I (-2 k + m) p + s (2 j - u)))] + (I a (-2 k + m) + (2 j - u) w) (I a (-2 k + m) + (2 j - u) w + 2 (I (-2 k + m) p + s (2 j - u)) Sqrt[z]) Gamma[1/2, -((I a (-2 k + m) + (2 j - u) w + 2 (I (-2 k + m) p + s (2 j - u)) Sqrt[z])^2/(4 (I (-2 k + m) p + s (2 j - u))))]))/((I (-2 k + m) p + s (2 j - u))^2 Sqrt[-((I a (-2 k + m) + (2 j - u) w + 2 (I (-2 k + m) p + s (2 j - u)) Sqrt[z])^2/(I (-2 k + m) p + s (2 j - u)))]) + (E^((I m Pi)/2 + I (2 k - m) q - (I Pi u)/2 + t (-2 j + u) - (I a (2 k - m) + (-2 j + u) w)^2/(4 (I (2 k - m) p + s (-2 j + u)))) (2 E^((I a (2 k - m) + (-2 j + u) w + 2 (I (2 k - m) p + s (-2 j + u)) Sqrt[z])^2/(4 (I (2 k - m) p + s (-2 j + u)))) (I (2 k - m) p + s (-2 j + u)) Sqrt[-((I a (2 k - m) + (-2 j + u) w + 2 (I (2 k - m) p + s (-2 j + u)) Sqrt[z])^2/ (I (2 k - m) p + s (-2 j + u)))] + (I a (2 k - m) + (-2 j + u) w) (I a (2 k - m) + (-2 j + u) w + 2 (I (2 k - m) p + s (-2 j + u)) Sqrt[z]) Gamma[1/2, -((I a (2 k - m) + (-2 j + u) w + 2 (I (2 k - m) p + s (-2 j + u)) Sqrt[z])^2/(4 (I (2 k - m) p + s (-2 j + u))))]))/((I (2 k - m) p + s (-2 j + u))^2 Sqrt[-((I a (2 k - m) + (-2 j + u) w + 2 (I (2 k - m) p + s (-2 j + u)) Sqrt[z])^2/(I (2 k - m) p + s (-2 j + u)))]) + (E^((-(1/2)) I m Pi + I (-2 k + m) q - (I Pi u)/2 + t (-2 j + u) - (I a (-2 k + m) + (-2 j + u) w)^2/ (4 (I (-2 k + m) p + s (-2 j + u)))) (2 E^((I a (-2 k + m) + (-2 j + u) w + 2 (I (-2 k + m) p + s (-2 j + u)) Sqrt[z])^2/(4 (I (-2 k + m) p + s (-2 j + u)))) (I (-2 k + m) p + s (-2 j + u)) Sqrt[-((I a (-2 k + m) + (-2 j + u) w + 2 (I (-2 k + m) p + s (-2 j + u)) Sqrt[z])^2/(I (-2 k + m) p + s (-2 j + u)))] + (I a (-2 k + m) + (-2 j + u) w) (I a (-2 k + m) + (-2 j + u) w + 2 (I (-2 k + m) p + s (-2 j + u)) Sqrt[z]) Gamma[1/2, -((I a (-2 k + m) + (-2 j + u) w + 2 (I (-2 k + m) p + s (-2 j + u)) Sqrt[z])^2/ (4 (I (-2 k + m) p + s (-2 j + u))))]))/ ((I (-2 k + m) p + s (-2 j + u))^2 Sqrt[-((I a (-2 k + m) + (-2 j + u) w + 2 (I (-2 k + m) p + s (-2 j + u)) Sqrt[z])^2/(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^((I m Pi)/2 + I (2 k - m) q - (I a (2 k - m) + c (2 h - v))^2/(4 (I (2 k - m) p + f (2 h - v))) + g (2 h - v)) (2 E^((I a (2 k - m) + c (2 h - v) + 2 (I (2 k - m) p + f (2 h - v)) Sqrt[z])^2/(4 (I (2 k - m) p + f (2 h - v)))) (I (2 k - m) p + f (2 h - v)) Sqrt[-((I a (2 k - m) + c (2 h - v) + 2 (I (2 k - m) p + f (2 h - v)) Sqrt[z])^2/ (I (2 k - m) p + f (2 h - v)))] + (I a (2 k - m) + c (2 h - v)) (I a (2 k - m) + c (2 h - v) + 2 (I (2 k - m) p + f (2 h - v)) Sqrt[z]) Gamma[1/2, -((I a (2 k - m) + c (2 h - v) + 2 (I (2 k - m) p + f (2 h - v)) Sqrt[z])^2/(4 (I (2 k - m) p + f (2 h - v))))]))/((I (2 k - m) p + f (2 h - v))^2 Sqrt[-((I a (2 k - m) + c (2 h - v) + 2 (I (2 k - m) p + f (2 h - v)) Sqrt[z])^2/(I (2 k - m) p + f (2 h - v)))]) + (E^((-(1/2)) I m Pi + I (-2 k + m) q - (I a (-2 k + m) + c (2 h - v))^2/(4 (I (-2 k + m) p + f (2 h - v))) + g (2 h - v)) (2 E^((I a (-2 k + m) + c (2 h - v) + 2 (I (-2 k + m) p + f (2 h - v)) Sqrt[z])^2/(4 (I (-2 k + m) p + f (2 h - v)))) (I (-2 k + m) p + f (2 h - v)) Sqrt[-((I a (-2 k + m) + c (2 h - v) + 2 (I (-2 k + m) p + f (2 h - v)) Sqrt[z])^2/ (I (-2 k + m) p + f (2 h - v)))] + (I a (-2 k + m) + c (2 h - v)) (I a (-2 k + m) + c (2 h - v) + 2 (I (-2 k + m) p + f (2 h - v)) Sqrt[z]) Gamma[1/2, -((I a (-2 k + m) + c (2 h - v) + 2 (I (-2 k + m) p + f (2 h - v)) Sqrt[z])^2/(4 (I (-2 k + m) p + f (2 h - v))))]))/((I (-2 k + m) p + f (2 h - v))^2 Sqrt[-((I a (-2 k + m) + c (2 h - v) + 2 (I (-2 k + m) p + f (2 h - v)) Sqrt[z])^2/(I (-2 k + m) p + f (2 h - v)))]) + (E^((I m Pi)/2 + I (2 k - m) q + g (-2 h + v) - (I a (2 k - m) + c (-2 h + v))^2/(4 (I (2 k - m) p + f (-2 h + v)))) (2 E^((I a (2 k - m) + c (-2 h + v) + 2 (I (2 k - m) p + f (-2 h + v)) Sqrt[z])^2/(4 (I (2 k - m) p + f (-2 h + v)))) (I (2 k - m) p + f (-2 h + v)) Sqrt[-((I a (2 k - m) + c (-2 h + v) + 2 (I (2 k - m) p + f (-2 h + v)) Sqrt[z])^2/ (I (2 k - m) p + f (-2 h + v)))] + (I a (2 k - m) + c (-2 h + v)) (I a (2 k - m) + c (-2 h + v) + 2 (I (2 k - m) p + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((I a (2 k - m) + c (-2 h + v) + 2 (I (2 k - m) p + f (-2 h + v)) Sqrt[z])^2/(4 (I (2 k - m) p + f (-2 h + v))))]))/((I (2 k - m) p + f (-2 h + v))^2 Sqrt[-((I a (2 k - m) + c (-2 h + v) + 2 (I (2 k - m) p + f (-2 h + v)) Sqrt[z])^2/(I (2 k - m) p + f (-2 h + v)))]) + (E^((-(1/2)) I m Pi + I (-2 k + m) q + g (-2 h + v) - (I a (-2 k + m) + c (-2 h + v))^2/ (4 (I (-2 k + m) p + f (-2 h + v)))) (2 E^((I a (-2 k + m) + c (-2 h + v) + 2 (I (-2 k + m) p + f (-2 h + v)) Sqrt[z])^2/(4 (I (-2 k + m) p + f (-2 h + v)))) (I (-2 k + m) p + f (-2 h + v)) Sqrt[-((I a (-2 k + m) + c (-2 h + v) + 2 (I (-2 k + m) p + f (-2 h + v)) Sqrt[z])^2/(I (-2 k + m) p + f (-2 h + v)))] + (I a (-2 k + m) + c (-2 h + v)) (I a (-2 k + m) + c (-2 h + v) + 2 (I (-2 k + m) p + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((I a (-2 k + m) + c (-2 h + v) + 2 (I (-2 k + m) p + f (-2 h + v)) Sqrt[z])^2/ (4 (I (-2 k + m) p + f (-2 h + v))))]))/ ((I (-2 k + m) p + f (-2 h + v))^2 Sqrt[-((I a (-2 k + m) + c (-2 h + v) + 2 (I (-2 k + m) p + f (-2 h + v)) Sqrt[z])^2/(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^(t (2 k - u) + (I Pi u)/2 + g (2 h - v) - (c (2 h - v) + (2 k - u) w)^2/(4 (s (2 k - u) + f (2 h - v)))) (2 E^((c (2 h - v) + (2 k - u) w + 2 (s (2 k - u) + f (2 h - v)) Sqrt[z])^2/(4 (s (2 k - u) + f (2 h - v)))) (s (2 k - u) + f (2 h - v)) Sqrt[-((c (2 h - v) + (2 k - u) w + 2 (s (2 k - u) + f (2 h - v)) Sqrt[z])^2/(s (2 k - u) + f (2 h - v)))] + (c (2 h - v) + (2 k - u) w) (c (2 h - v) + (2 k - u) w + 2 (s (2 k - u) + f (2 h - v)) Sqrt[ z]) Gamma[1/2, -((c (2 h - v) + (2 k - u) w + 2 (s (2 k - u) + f (2 h - v)) Sqrt[z])^2/(4 (s (2 k - u) + f (2 h - v))))]))/((s (2 k - u) + f (2 h - v))^2 Sqrt[-((c (2 h - v) + (2 k - u) w + 2 (s (2 k - u) + f (2 h - v)) Sqrt[z])^2/(s (2 k - u) + f (2 h - v)))]) + (E^((-(1/2)) I Pi u + t (-2 k + u) + g (2 h - v) - (c (2 h - v) + (-2 k + u) w)^2/(4 (s (-2 k + u) + f (2 h - v)))) (2 E^((c (2 h - v) + (-2 k + u) w + 2 (s (-2 k + u) + f (2 h - v)) Sqrt[z])^2/(4 (s (-2 k + u) + f (2 h - v)))) (s (-2 k + u) + f (2 h - v)) Sqrt[-((c (2 h - v) + (-2 k + u) w + 2 (s (-2 k + u) + f (2 h - v)) Sqrt[z])^2/ (s (-2 k + u) + f (2 h - v)))] + (c (2 h - v) + (-2 k + u) w) (c (2 h - v) + (-2 k + u) w + 2 (s (-2 k + u) + f (2 h - v)) Sqrt[z]) Gamma[1/2, -((c (2 h - v) + (-2 k + u) w + 2 (s (-2 k + u) + f (2 h - v)) Sqrt[z])^2/ (4 (s (-2 k + u) + f (2 h - v))))]))/ ((s (-2 k + u) + f (2 h - v))^2 Sqrt[-((c (2 h - v) + (-2 k + u) w + 2 (s (-2 k + u) + f (2 h - v)) Sqrt[z])^2/(s (-2 k + u) + f (2 h - v)))]) + (E^(t (2 k - u) + (I Pi u)/2 + g (-2 h + v) - (c (-2 h + v) + (2 k - u) w)^2/(4 (s (2 k - u) + f (-2 h + v)))) (2 E^((c (-2 h + v) + (2 k - u) w + 2 (s (2 k - u) + f (-2 h + v)) Sqrt[z])^2/(4 (s (2 k - u) + f (-2 h + v)))) (s (2 k - u) + f (-2 h + v)) Sqrt[-((c (-2 h + v) + (2 k - u) w + 2 (s (2 k - u) + f (-2 h + v)) Sqrt[z])^2/ (s (2 k - u) + f (-2 h + v)))] + (c (-2 h + v) + (2 k - u) w) (c (-2 h + v) + (2 k - u) w + 2 (s (2 k - u) + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((c (-2 h + v) + (2 k - u) w + 2 (s (2 k - u) + f (-2 h + v)) Sqrt[z])^2/ (4 (s (2 k - u) + f (-2 h + v))))]))/ ((s (2 k - u) + f (-2 h + v))^2 Sqrt[-((c (-2 h + v) + (2 k - u) w + 2 (s (2 k - u) + f (-2 h + v)) Sqrt[z])^2/(s (2 k - u) + f (-2 h + v)))]) + (E^((-(1/2)) I Pi u + t (-2 k + u) + g (-2 h + v) - (c (-2 h + v) + (-2 k + u) w)^2/(4 (s (-2 k + u) + f (-2 h + v)))) (2 E^((c (-2 h + v) + (-2 k + u) w + 2 (s (-2 k + u) + f (-2 h + v)) Sqrt[z])^2/(4 (s (-2 k + u) + f (-2 h + v)))) (s (-2 k + u) + f (-2 h + v)) Sqrt[-((c (-2 h + v) + (-2 k + u) w + 2 (s (-2 k + u) + f (-2 h + v)) Sqrt[z])^2/(s (-2 k + u) + f (-2 h + v)))] + (c (-2 h + v) + (-2 k + u) w) (c (-2 h + v) + (-2 k + u) w + 2 (s (-2 k + u) + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((c (-2 h + v) + (-2 k + u) w + 2 (s (-2 k + u) + f (-2 h + v)) Sqrt[z])^2/ (4 (s (-2 k + u) + f (-2 h + v))))]))/ ((s (-2 k + u) + f (-2 h + v))^2 Sqrt[-((c (-2 h + v) + (-2 k + u) w + 2 (s (-2 k + u) + f (-2 h + v)) Sqrt[z])^2/(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^((I m Pi)/2 + I (2 k - m) q + t (2 j - u) + (I Pi u)/2 + g (2 h - v) - (I a (2 k - m) + c (2 h - v) + (2 j - u) w)^2/ (4 (I (2 k - m) p + s (2 j - u) + f (2 h - v)))) (2 E^((I a (2 k - m) + c (2 h - v) + (2 j - u) w + 2 (I (2 k - m) p + s (2 j - u) + f (2 h - v)) Sqrt[z])^2/ (4 (I (2 k - m) p + s (2 j - u) + f (2 h - v)))) ( I (2 k - m) p + s (2 j - u) + f (2 h - v)) Sqrt[ -((I a (2 k - m) + c (2 h - v) + (2 j - u) w + 2 (I (2 k - m) p + s (2 j - u) + f (2 h - v)) Sqrt[z])^2/ (I (2 k - m) p + s (2 j - u) + f (2 h - v)))] + (I a (2 k - m) + c (2 h - v) + (2 j - u) w) (I a (2 k - m) + c (2 h - v) + (2 j - u) w + 2 (I (2 k - m) p + s (2 j - u) + f (2 h - v)) Sqrt[z]) Gamma[1/2, -((I a (2 k - m) + c (2 h - v) + (2 j - u) w + 2 (I (2 k - m) p + s (2 j - u) + f (2 h - v)) Sqrt[z])^2/ (4 (I (2 k - m) p + s (2 j - u) + f (2 h - v))))]))/ ((I (2 k - m) p + s (2 j - u) + f (2 h - v))^2 Sqrt[-((I a (2 k - m) + c (2 h - v) + (2 j - u) w + 2 (I (2 k - m) p + s (2 j - u) + f (2 h - v)) Sqrt[z])^2/ (I (2 k - m) p + s (2 j - u) + f (2 h - v)))]) + (E^((-(1/2)) I m Pi + I (-2 k + m) q + t (2 j - u) + (I Pi u)/2 + g (2 h - v) - (I a (-2 k + m) + c (2 h - v) + (2 j - u) w)^2/ (4 (I (-2 k + m) p + s (2 j - u) + f (2 h - v)))) (2 E^((I a (-2 k + m) + c (2 h - v) + (2 j - u) w + 2 (I (-2 k + m) p + s (2 j - u) + f (2 h - v)) Sqrt[z])^2/ (4 (I (-2 k + m) p + s (2 j - u) + f (2 h - v)))) ( I (-2 k + m) p + s (2 j - u) + f (2 h - v)) Sqrt[ -((I a (-2 k + m) + c (2 h - v) + (2 j - u) w + 2 (I (-2 k + m) p + s (2 j - u) + f (2 h - v)) Sqrt[z])^2/ (I (-2 k + m) p + s (2 j - u) + f (2 h - v)))] + (I a (-2 k + m) + c (2 h - v) + (2 j - u) w) (I a (-2 k + m) + c (2 h - v) + (2 j - u) w + 2 (I (-2 k + m) p + s (2 j - u) + f (2 h - v)) Sqrt[z]) Gamma[1/2, -((I a (-2 k + m) + c (2 h - v) + (2 j - u) w + 2 (I (-2 k + m) p + s (2 j - u) + f (2 h - v)) Sqrt[z])^2/ (4 (I (-2 k + m) p + s (2 j - u) + f (2 h - v))))]))/ ((I (-2 k + m) p + s (2 j - u) + f (2 h - v))^2 Sqrt[-((I a (-2 k + m) + c (2 h - v) + (2 j - u) w + 2 (I (-2 k + m) p + s (2 j - u) + f (2 h - v)) Sqrt[z])^2/ (I (-2 k + m) p + s (2 j - u) + f (2 h - v)))]) + (E^((I m Pi)/2 + I (2 k - m) q - (I Pi u)/2 + t (-2 j + u) + g (2 h - v) - (I a (2 k - m) + c (2 h - v) + (-2 j + u) w)^2/ (4 (I (2 k - m) p + s (-2 j + u) + f (2 h - v)))) (2 E^((I a (2 k - m) + c (2 h - v) + (-2 j + u) w + 2 (I (2 k - m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z])^2/ (4 (I (2 k - m) p + s (-2 j + u) + f (2 h - v)))) ( I (2 k - m) p + s (-2 j + u) + f (2 h - v)) Sqrt[ -((I a (2 k - m) + c (2 h - v) + (-2 j + u) w + 2 (I (2 k - m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z])^2/ (I (2 k - m) p + s (-2 j + u) + f (2 h - v)))] + (I a (2 k - m) + c (2 h - v) + (-2 j + u) w) (I a (2 k - m) + c (2 h - v) + (-2 j + u) w + 2 (I (2 k - m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z]) Gamma[1/2, -((I a (2 k - m) + c (2 h - v) + (-2 j + u) w + 2 (I (2 k - m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z])^2/ (4 (I (2 k - m) p + s (-2 j + u) + f (2 h - v))))]))/ ((I (2 k - m) p + s (-2 j + u) + f (2 h - v))^2 Sqrt[-((I a (2 k - m) + c (2 h - v) + (-2 j + u) w + 2 (I (2 k - m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z])^2/ (I (2 k - m) p + s (-2 j + u) + f (2 h - v)))]) + (E^((-(1/2)) I m Pi + I (-2 k + m) q - (I Pi u)/2 + t (-2 j + u) + g (2 h - v) - (I a (-2 k + m) + c (2 h - v) + (-2 j + u) w)^2/ (4 (I (-2 k + m) p + s (-2 j + u) + f (2 h - v)))) (2 E^((I a (-2 k + m) + c (2 h - v) + (-2 j + u) w + 2 (I (-2 k + m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z])^2/ (4 (I (-2 k + m) p + s (-2 j + u) + f (2 h - v)))) ( I (-2 k + m) p + s (-2 j + u) + f (2 h - v)) Sqrt[ -((I a (-2 k + m) + c (2 h - v) + (-2 j + u) w + 2 (I (-2 k + m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z])^ 2/(I (-2 k + m) p + s (-2 j + u) + f (2 h - v)))] + (I a (-2 k + m) + c (2 h - v) + (-2 j + u) w) (I a (-2 k + m) + c (2 h - v) + (-2 j + u) w + 2 (I (-2 k + m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z]) Gamma[1/2, -((I a (-2 k + m) + c (2 h - v) + (-2 j + u) w + 2 (I (-2 k + m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z])^ 2/(4 (I (-2 k + m) p + s (-2 j + u) + f (2 h - v))))]))/ ((I (-2 k + m) p + s (-2 j + u) + f (2 h - v))^2 Sqrt[-((I a (-2 k + m) + c (2 h - v) + (-2 j + u) w + 2 (I (-2 k + m) p + s (-2 j + u) + f (2 h - v)) Sqrt[z])^2/ (I (-2 k + m) p + s (-2 j + u) + f (2 h - v)))]) + (E^((I m Pi)/2 + I (2 k - m) q + t (2 j - u) + (I Pi u)/2 + g (-2 h + v) - (I a (2 k - m) + c (-2 h + v) + (2 j - u) w)^2/ (4 (I (2 k - m) p + s (2 j - u) + f (-2 h + v)))) (2 E^((I a (2 k - m) + c (-2 h + v) + (2 j - u) w + 2 (I (2 k - m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z])^2/ (4 (I (2 k - m) p + s (2 j - u) + f (-2 h + v)))) ( I (2 k - m) p + s (2 j - u) + f (-2 h + v)) Sqrt[ -((I a (2 k - m) + c (-2 h + v) + (2 j - u) w + 2 (I (2 k - m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z])^2/ (I (2 k - m) p + s (2 j - u) + f (-2 h + v)))] + (I a (2 k - m) + c (-2 h + v) + (2 j - u) w) (I a (2 k - m) + c (-2 h + v) + (2 j - u) w + 2 (I (2 k - m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((I a (2 k - m) + c (-2 h + v) + (2 j - u) w + 2 (I (2 k - m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z])^2/ (4 (I (2 k - m) p + s (2 j - u) + f (-2 h + v))))]))/ ((I (2 k - m) p + s (2 j - u) + f (-2 h + v))^2 Sqrt[-((I a (2 k - m) + c (-2 h + v) + (2 j - u) w + 2 (I (2 k - m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z])^2/ (I (2 k - m) p + s (2 j - u) + f (-2 h + v)))]) + (E^((-(1/2)) I m Pi + I (-2 k + m) q + t (2 j - u) + (I Pi u)/2 + g (-2 h + v) - (I a (-2 k + m) + c (-2 h + v) + (2 j - u) w)^2/ (4 (I (-2 k + m) p + s (2 j - u) + f (-2 h + v)))) (2 E^((I a (-2 k + m) + c (-2 h + v) + (2 j - u) w + 2 (I (-2 k + m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z])^2/ (4 (I (-2 k + m) p + s (2 j - u) + f (-2 h + v)))) ( I (-2 k + m) p + s (2 j - u) + f (-2 h + v)) Sqrt[ -((I a (-2 k + m) + c (-2 h + v) + (2 j - u) w + 2 (I (-2 k + m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z])^ 2/(I (-2 k + m) p + s (2 j - u) + f (-2 h + v)))] + (I a (-2 k + m) + c (-2 h + v) + (2 j - u) w) (I a (-2 k + m) + c (-2 h + v) + (2 j - u) w + 2 (I (-2 k + m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((I a (-2 k + m) + c (-2 h + v) + (2 j - u) w + 2 (I (-2 k + m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z])^ 2/(4 (I (-2 k + m) p + s (2 j - u) + f (-2 h + v))))]))/ ((I (-2 k + m) p + s (2 j - u) + f (-2 h + v))^2 Sqrt[-((I a (-2 k + m) + c (-2 h + v) + (2 j - u) w + 2 (I (-2 k + m) p + s (2 j - u) + f (-2 h + v)) Sqrt[z])^2/ (I (-2 k + m) p + s (2 j - u) + f (-2 h + v)))]) + (E^((I m Pi)/2 + I (2 k - m) q - (I Pi u)/2 + t (-2 j + u) + g (-2 h + v) - (I a (2 k - m) + c (-2 h + v) + (-2 j + u) w)^2/ (4 (I (2 k - m) p + s (-2 j + u) + f (-2 h + v)))) (2 E^((I a (2 k - m) + c (-2 h + v) + (-2 j + u) w + 2 (I (2 k - m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z])^2/ (4 (I (2 k - m) p + s (-2 j + u) + f (-2 h + v)))) ( I (2 k - m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[ -((I a (2 k - m) + c (-2 h + v) + (-2 j + u) w + 2 (I (2 k - m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z])^ 2/(I (2 k - m) p + s (-2 j + u) + f (-2 h + v)))] + (I a (2 k - m) + c (-2 h + v) + (-2 j + u) w) (I a (2 k - m) + c (-2 h + v) + (-2 j + u) w + 2 (I (2 k - m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((I a (2 k - m) + c (-2 h + v) + (-2 j + u) w + 2 (I (2 k - m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z])^ 2/(4 (I (2 k - m) p + s (-2 j + u) + f (-2 h + v))))]))/ ((I (2 k - m) p + s (-2 j + u) + f (-2 h + v))^2 Sqrt[-((I a (2 k - m) + c (-2 h + v) + (-2 j + u) w + 2 (I (2 k - m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z])^2/ (I (2 k - m) p + s (-2 j + u) + f (-2 h + v)))]) + (E^((-(1/2)) I m Pi + I (-2 k + m) q - (I Pi u)/2 + t (-2 j + u) + g (-2 h + v) - (I a (-2 k + m) + c (-2 h + v) + (-2 j + u) w)^ 2/(4 (I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)))) (2 E^((I a (-2 k + m) + c (-2 h + v) + (-2 j + u) w + 2 (I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z])^ 2/(4 (I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)))) ( I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[ -((I a (-2 k + m) + c (-2 h + v) + (-2 j + u) w + 2 (I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z])^ 2/(I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)))] + (I a (-2 k + m) + c (-2 h + v) + (-2 j + u) w) ( I a (-2 k + m) + c (-2 h + v) + (-2 j + u) w + 2 (I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z]) Gamma[1/2, -((I a (-2 k + m) + c (-2 h + v) + (-2 j + u) w + 2 (I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z])^ 2/(4 (I (-2 k + m) p + s (-2 j + u) + f (-2 h + v))))]))/ ((I (-2 k + m) p + s (-2 j + u) + f (-2 h + v))^2 Sqrt[-((I a (-2 k + m) + c (-2 h + v) + (-2 j + u) w + 2 (I (-2 k + m) p + s (-2 j + u) + f (-2 h + v)) Sqrt[z])^2/ (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

 sin m ( z a + p z + q ) sinh u ( w z + s z + t ) cosh v ( z c + f z + g ) z u 2 - m - u - v z ( 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 ) - 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]]]]] ( ( - ( 2 k - m ) a 2 4 p + ( 2 k - m ) q + m π 2 ( 2 - ( a ( 2 k - m ) + 2 p z ( 2 k - m ) ) 2 4 ( 2 k - m ) p ( 2 k - m ) ( a ( 2 k - m ) + 2 p z ( 2 k - m ) ) 2 ( 2 k - m ) p p + a ( 2 k - m ) ( a ( 2 k - m ) + 2 p z ( 2 k - m ) ) Γ ( 1 2 , ( a ( 2 k - m ) + 2 p z ( 2 k - m ) ) 2 4 ( 2 k - m ) p ) ) ) / ( ( 2 k - m ) 2 p 2 ( a ( 2 k - m ) + 2 p z ( 2 k - m ) ) 2 ( 2 k - m ) p ) + ( - ( m - 2 k ) a 2 4 p + ( m - 2 k ) q - m π 2 ( 2 - ( a ( m - 2 k ) + 2 p z ( m - 2 k ) ) 2 4 ( m - 2 k ) p ( m - 2 k ) ( a ( m - 2 k ) + 2 p z ( m - 2 k ) ) 2 ( m - 2 k ) p p + a ( m - 2 k ) ( a ( m - 2 k ) + 2 p z ( m - 2 k ) ) Γ ( 1 2 , ( a ( m - 2 k ) + 2 p z ( m - 2 k ) ) 2 4 ( m - 2 k ) p ) ) ) / ( ( m - 2 k ) 2 p 2 ( a ( m - 2 k ) + 2 p z ( m - 2 k ) ) 2 ( 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]]]]] ( ( - ( 2 k - u ) w 2 4 s + t ( 2 k - u ) + π u 2 ( w ( w ( 2 k - u ) + 2 s z ( 2 k - u ) ) Γ ( 1 2 , - ( w ( 2 k - u ) + 2 s z ( 2 k - u ) ) 2 4 s ( 2 k - u ) ) ( 2 k - u ) + 2 ( w ( 2 k - u ) + 2 s z ( 2 k - u ) ) 2 4 s ( 2 k - u ) s - ( w ( 2 k - u ) + 2 s z ( 2 k - u ) ) 2 s ( 2 k - u ) ( 2 k - u ) ) ) / ( s 2 ( 2 k - u ) 2 - ( w ( 2 k - u ) + 2 s z ( 2 k - u ) ) 2 s ( 2 k - u ) ) + ( - ( u - 2 k ) w 2 4 s - π u 2 + t ( u - 2 k ) ( w ( w ( u - 2 k ) + 2 s z ( u - 2 k ) ) Γ ( 1 2 , - ( w ( u - 2 k ) + 2 s z ( u - 2 k ) ) 2 4 s ( u - 2 k ) ) ( u - 2 k ) + 2 ( w ( u - 2 k ) + 2 s z ( u - 2 k ) ) 2 4 s ( u - 2 k ) s - ( w ( u - 2 k ) + 2 s z ( u - 2 k ) ) 2 s ( u - 2 k ) ( u - 2 k ) ) ) / ( s 2 ( u - 2 k ) 2 - ( w ( u - 2 k ) + 2 s z ( u - 2 k ) ) 2 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]]]]] ( ( g ( 2 h - v ) - c 2 ( 2 h - v ) 4 f ( c ( c ( 2 h - v ) + 2 f z ( 2 h - v ) ) Γ ( 1 2 , - ( c ( 2 h - v ) + 2 f z ( 2 h - v ) ) 2 4 f ( 2 h - v ) ) ( 2 h - v ) + 2 ( c ( 2 h - v ) + 2 f z ( 2 h - v ) ) 2 4 f ( 2 h - v ) f - ( c ( 2 h - v ) + 2 f z ( 2 h - v ) ) 2 f ( 2 h - v ) ( 2 h - v ) ) ) / ( f 2 ( 2 h - v ) 2 - ( c ( 2 h - v ) + 2 f z ( 2 h - v ) ) 2 f ( 2 h - v ) ) + ( g ( v - 2 h ) - c 2 ( v - 2 h ) 4 f ( c ( c ( v - 2 h ) + 2 f z ( v - 2 h ) ) Γ ( 1 2 , - ( c ( v - 2 h ) + 2 f z ( v - 2 h ) ) 2 4 f ( v - 2 h ) ) ( v - 2 h ) + 2 ( c ( v - 2 h ) + 2 f z ( v - 2 h ) ) 2 4 f ( v - 2 h ) f - ( c ( v - 2 h ) + 2 f z ( v - 2 h ) ) 2 f ( v - 2 h ) ( v - 2 h ) ) ) / ( f 2 ( v - 2 h ) 2 - ( c ( v - 2 h ) + 2 f z ( v - 2 h ) ) 2 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]]]]] ( ( - ( a ( 2 k - m ) + ( 2 j - u ) w ) 2 4 ( ( 2 k - m ) p + s ( 2 j - u ) ) + ( 2 k - m ) q + t ( 2 j - u ) + π u 2 + m π 2 ( ( a ( 2 k - m ) + ( 2 j - u ) w ) ( a ( 2 k - m ) + ( 2 j - u ) w + 2 ( ( 2 k - m ) p + s ( 2 j - u ) ) z ) Γ ( 1 2 , - ( a ( 2 k - m ) + ( 2 j - u ) w + 2 ( ( 2 k - m ) p + s ( 2 j - u ) ) z ) 2 / ( 4 ( ( 2 k - m ) p + s ( 2 j - u ) ) ) ) + 2 ( a ( 2 k - m ) + ( 2 j - u ) w + 2 ( ( 2 k - m ) p + s ( 2 j - u ) ) z ) 2 4 ( ( 2 k - m ) p + s ( 2 j - u ) ) ( ( 2 k - m ) p + s ( 2 j - u ) ) ( - ( a ( 2 k - m ) + ( 2 j - u ) w + 2 ( ( 2 k - m ) p + s ( 2 j - u ) ) z ) 2 / ( ( 2 k - m ) p + s ( 2 j - u ) ) ) ) ) / ( ( ( 2 k - m ) p + s ( 2 j - u ) ) 2 - ( a ( 2 k - m ) + ( 2 j - u ) w + 2 ( ( 2 k - m ) p + s ( 2 j - u ) ) z ) 2 ( 2 k - m ) p + s ( 2 j - u ) ) + ( - ( a ( m - 2 k ) + ( 2 j - u ) w ) 2 4 ( ( m - 2 k ) p + s ( 2 j - u ) ) + ( m - 2 k ) q + t ( 2 j - u ) + π u 2 - m π 2 ( ( a ( m - 2 k ) + ( 2 j - u ) w ) ( a ( m - 2 k ) + ( 2 j - u ) w + 2 ( ( m - 2 k ) p + s ( 2 j - u ) ) z ) Γ ( 1 2 , - ( a ( m - 2 k ) + ( 2 j - u ) w + 2 ( ( m - 2 k ) p + s ( 2 j - u ) ) z ) 2 / ( 4 ( ( m - 2 k ) p + s ( 2 j - u ) ) ) ) + 2 ( a ( m - 2 k ) + ( 2 j - u ) w + 2 ( ( m - 2 k ) p + s ( 2 j - u ) ) z ) 2 4 ( ( m - 2 k ) p + s ( 2 j - u ) ) ( ( m - 2 k ) p + s ( 2 j - u ) ) ( - ( a ( m - 2 k ) + ( 2 j - u ) w + 2 ( ( m - 2 k ) p + s ( 2 j - u ) ) z ) 2 / ( ( m - 2 k ) p + s ( 2 j - u ) ) ) ) ) / ( ( ( m - 2 k ) p + s ( 2 j - u ) ) 2 - ( a ( m - 2 k ) + ( 2 j - u ) w + 2 ( ( m - 2 k ) p + s ( 2 j - u ) ) z ) 2 ( m - 2 k ) p + s ( 2 j - u ) ) + ( - ( a ( 2 k - m ) + ( u - 2 j ) w ) 2 4 ( ( 2 k - m ) p + s ( u - 2 j ) ) + ( 2 k - m ) q + t ( u - 2 j ) - π u 2 + m π 2 ( ( a ( 2 k - m ) + ( u - 2 j ) w ) ( a ( 2 k - m ) + ( u - 2 j ) w + 2 ( ( 2 k - m ) p + s ( u - 2 j ) ) z ) Γ ( 1 2 , - ( a ( 2 k - m ) + ( u - 2 j ) w + 2 ( ( 2 k - m ) p + s ( u - 2 j ) ) z ) 2 / ( 4 ( ( 2 k - m ) p + s ( u - 2 j ) ) ) ) + 2 ( a ( 2 k - m ) + ( u - 2 j ) w + 2 ( ( 2 k - m ) p + s ( u - 2 j ) ) z ) 2 4 ( ( 2 k - m ) p + s ( u - 2 j ) ) ( ( 2 k - m ) p + s ( u - 2 j ) ) ( - ( a ( 2 k - m ) + ( u - 2 j ) w + 2 ( ( 2 k - m ) p + s ( u - 2 j ) ) z ) 2 / ( ( 2 k - m ) p + s ( u - 2 j ) ) ) ) ) / ( ( ( 2 k - m ) p + s ( u - 2 j ) ) 2 - ( a ( 2 k - m ) + ( u - 2 j ) w + 2 ( ( 2 k - m ) p + s ( u - 2 j ) ) z ) 2 ( 2 k - m ) p + s ( u - 2 j ) ) + ( - ( a ( m - 2 k ) + ( u - 2 j ) w ) 2 4 ( ( m - 2 k ) p + s ( u - 2 j ) ) + ( m - 2 k ) q + t ( u - 2 j ) - π u 2 - m π 2 ( ( a ( m - 2 k ) + ( u - 2 j ) w ) ( a ( m - 2 k ) + ( u - 2 j ) w + 2 ( ( m - 2 k ) p + s ( u - 2 j ) ) z ) Γ ( 1 2 , - ( a ( m - 2 k ) + ( u - 2 j ) w + 2 ( ( m - 2 k ) p + s ( u - 2 j ) ) z ) 2 / ( 4 ( ( m - 2 k ) p + s ( u - 2 j ) ) ) ) + 2 ( a ( m - 2 k ) + ( u - 2 j ) w + 2 ( ( m - 2 k ) p + s ( u - 2 j ) ) z ) 2 4 ( ( m - 2 k ) p + s ( u - 2 j ) ) ( ( m - 2 k ) p + s ( u - 2 j ) ) ( - ( a ( m - 2 k ) + ( u - 2 j ) w + 2 ( ( m - 2 k ) p + s ( u - 2 j ) ) z ) 2 / ( ( m - 2 k ) p + s ( u - 2 j ) ) ) ) ) / ( ( ( m - 2 k ) p + s ( u - 2 j ) ) 2 - ( a ( m - 2 k ) + ( u - 2 j ) w + 2 ( ( m - 2 k ) p + s ( u - 2 j ) ) z ) 2 ( 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]]]]] ( ( - ( a ( 2 k - m ) + c ( 2 h - v ) ) 2 4 ( ( 2 k - m ) p + f ( 2 h - v ) ) + ( 2 k - m ) q + g ( 2 h - v ) + m π 2 ( ( a ( 2 k - m ) + c ( 2 h - v ) ) ( a ( 2 k - m ) + c ( 2 h - v ) + 2 ( ( 2 k - m ) p + f ( 2 h - v ) ) z ) Γ ( 1 2 , - ( a ( 2 k - m ) + c ( 2 h - v ) + 2 ( ( 2 k - m ) p + f ( 2 h - v ) ) z ) 2 / ( 4 ( ( 2 k - m ) p + f ( 2 h - v ) ) ) ) + 2 ( a ( 2 k - m ) + c ( 2 h - v ) + 2 ( ( 2 k - m ) p + f ( 2 h - v ) ) z ) 2 4 ( ( 2 k - m ) p + f ( 2 h - v ) ) ( ( 2 k - m ) p + f ( 2 h - v ) ) ( - ( a ( 2 k - m ) + c ( 2 h - v ) + 2 ( ( 2 k - m ) p + f ( 2 h - v ) ) z ) 2 / ( ( 2 k - m ) p + f ( 2 h - v ) ) ) ) ) / ( ( ( 2 k - m ) p + f ( 2 h - v ) ) 2 - ( a ( 2 k - m ) + c ( 2 h - v ) + 2 ( ( 2 k - m ) p + f ( 2 h - v ) ) z ) 2 ( 2 k - m ) p + f ( 2 h - v ) ) + ( - ( a ( m - 2 k ) + c ( 2 h - v ) ) 2 4 ( ( m - 2 k ) p + f ( 2 h - v ) ) + ( m - 2 k ) q + g ( 2 h - v ) - m π 2 ( ( a ( m - 2 k ) + c ( 2 h - v ) ) ( a ( m - 2 k ) + c ( 2 h - v ) + 2 ( ( m - 2 k ) p + f ( 2 h - v ) ) z ) Γ ( 1 2 , - ( a ( m - 2 k ) + c ( 2 h - v ) + 2 ( ( m - 2 k ) p + f ( 2 h - v ) ) z ) 2 / ( 4 ( ( m - 2 k ) p + f ( 2 h - v ) ) ) ) + 2 ( a ( m - 2 k ) + c ( 2 h - v ) + 2 ( ( m - 2 k ) p + f ( 2 h - v ) ) z ) 2 4 ( ( m - 2 k ) p + f ( 2 h - v ) ) ( ( m - 2 k ) p + f ( 2 h - v ) ) ( - ( a ( m - 2 k ) + c ( 2 h - v ) + 2 ( ( m - 2 k ) p + f ( 2 h - v ) ) z ) 2 / ( ( m - 2 k ) p + f ( 2 h - v ) ) ) ) ) / ( ( ( m - 2 k ) p + f ( 2 h - v ) ) 2 - ( a ( m - 2 k ) + c ( 2 h - v ) + 2 ( ( m - 2 k ) p + f ( 2 h - v ) ) z ) 2 ( m - 2 k ) p + f ( 2 h - v ) ) + ( - ( a ( 2 k - m ) + c ( v - 2 h ) ) 2 4 ( ( 2 k - m ) p + f ( v - 2 h ) ) + ( 2 k - m ) q + g ( v - 2 h ) + m π 2 ( ( a ( 2 k - m ) + c ( v - 2 h ) ) ( a ( 2 k - m ) + c ( v - 2 h ) + 2 ( ( 2 k - m ) p + f ( v - 2 h ) ) z ) Γ ( 1 2 , - ( a ( 2 k - m ) + c ( v - 2 h ) + 2 ( ( 2 k - m ) p + f ( v - 2 h ) ) z ) 2 / ( 4 ( ( 2 k - m ) p + f ( v - 2 h ) ) ) ) + 2 ( a ( 2 k - m ) + c ( v - 2 h ) + 2 ( ( 2 k - m ) p + f ( v - 2 h ) ) z ) 2 4 ( ( 2 k - m ) p + f ( v - 2 h ) ) ( ( 2 k - m ) p + f ( v - 2 h ) ) ( - ( a ( 2 k - m ) + c ( v - 2 h ) + 2 ( ( 2 k - m ) p + f ( v - 2 h ) ) z ) 2 / ( ( 2 k - m ) p + f ( v - 2 h ) ) ) ) ) / ( ( ( 2 k - m ) p + f ( v - 2 h ) ) 2 - ( a ( 2 k - m ) + c ( v - 2 h ) + 2 ( ( 2 k - m ) p + f ( v - 2 h ) ) z ) 2 ( 2 k - m ) p + f ( v - 2 h ) ) + ( - ( a ( m - 2 k ) + c ( v - 2 h ) ) 2 4 ( ( m - 2 k ) p + f ( v - 2 h ) ) + ( m - 2 k ) q + g ( v - 2 h ) - m π 2 ( ( a ( m - 2 k ) + c ( v - 2 h ) ) ( a ( m - 2 k ) + c ( v - 2 h ) + 2 ( ( m - 2 k ) p + f ( v - 2 h ) ) z ) Γ ( 1 2 , - ( a ( m - 2 k ) + c ( v - 2 h ) + 2 ( ( m - 2 k ) p + f ( v - 2 h ) ) z ) 2 / ( 4 ( ( m - 2 k ) p + f ( v - 2 h ) ) ) ) + 2 ( a ( m - 2 k ) + c ( v - 2 h ) + 2 ( ( m - 2 k ) p + f ( v - 2 h ) ) z ) 2 4 ( ( m - 2 k ) p + f ( v - 2 h ) ) ( ( m - 2 k ) p + f ( v - 2 h ) ) ( - ( a ( m - 2 k ) + c ( v - 2 h ) + 2 ( ( m - 2 k ) p + f ( v - 2 h ) ) z ) 2 / ( ( m - 2 k ) p + f ( v - 2 h ) ) ) ) ) / ( ( ( m - 2 k ) p + f ( v - 2 h ) ) 2 - ( a ( m - 2 k ) + c ( v - 2 h ) + 2 ( ( m - 2 k ) p + f ( v - 2 h ) ) z ) 2 ( 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]]]]] ( ( - ( c ( 2 h - v ) + ( 2 k - u ) w ) 2 4 ( s ( 2 k - u ) + f ( 2 h - v ) ) + t ( 2 k - u ) + π u 2 + g ( 2 h - v ) ( ( c ( 2 h - v ) + ( 2 k - u ) w ) ( 2 z ( s ( 2 k - u ) + f ( 2 h - v ) ) + c ( 2 h - v ) + ( 2 k - u ) w ) Γ ( 1 2 , - ( 2 z ( s ( 2 k - u ) + f ( 2 h - v ) ) + c ( 2 h - v ) + ( 2 k - u ) w ) 2 4 ( s ( 2 k - u ) + f ( 2 h - v ) ) ) + 2 ( 2 z ( s ( 2 k - u ) + f ( 2 h - v ) ) + c ( 2 h - v ) + ( 2 k - u ) w ) 2 4 ( s ( 2 k - u ) + f ( 2 h - v ) ) ( s ( 2 k - u ) + f ( 2 h - v ) ) ( - ( 2 z ( s ( 2 k - u ) + f ( 2 h - v ) ) + c ( 2 h - v ) + ( 2 k - u ) w ) 2 / ( s ( 2 k - u ) + f ( 2 h - v ) ) ) ) ) / ( ( s ( 2 k - u ) + f ( 2 h - v ) ) 2 - ( 2 z ( s ( 2 k - u ) + f ( 2 h - v ) ) + c ( 2 h - v ) + ( 2 k - u ) w ) 2 s ( 2 k - u ) + f ( 2 h - v ) ) + ( - ( c ( 2 h - v ) + ( u - 2 k ) w ) 2 4 ( s ( u - 2 k ) + f ( 2 h - v ) ) - π u 2 + t ( u - 2 k ) + g ( 2 h - v ) ( ( c ( 2 h - v ) + ( u - 2 k ) w ) ( 2 z ( s ( u - 2 k ) + f ( 2 h - v ) ) + c ( 2 h - v ) + ( u - 2 k ) w ) Γ ( 1 2 , - ( 2 z ( s ( u - 2 k ) + f ( 2 h - v ) ) + c ( 2 h - v ) + ( u - 2 k ) w ) 2 4 ( s ( u - 2 k ) + f ( 2 h - v ) ) ) + 2 ( 2 z ( s ( u - 2 k ) + f ( 2 h - v ) ) + c ( 2 h - v ) + ( u - 2 k ) w ) 2 4 ( s ( u - 2 k ) + f ( 2 h - v ) ) ( s ( u - 2 k ) + f ( 2 h - v ) ) ( - ( 2 z ( s ( u - 2 k ) + f ( 2 h - v ) ) + c ( 2 h - v ) + ( u - 2 k ) w ) 2 / ( s ( u - 2 k ) + f ( 2 h - v ) ) ) ) ) / ( ( s ( u - 2 k ) + f ( 2 h - v ) ) 2 - ( 2 z ( s ( u - 2 k ) + f ( 2 h - v ) ) + c ( 2 h - v ) + ( u - 2 k ) w ) 2 s ( u - 2 k ) + f ( 2 h - v ) ) + ( - ( c ( v - 2 h ) + ( 2 k - u ) w ) 2 4 ( s ( 2 k - u ) + f ( v - 2 h ) ) + t ( 2 k - u ) + π u 2 + g ( v - 2 h ) ( ( c ( v - 2 h ) + ( 2 k - u ) w ) ( c ( v - 2 h ) + ( 2 k - u ) w + 2 ( s ( 2 k - u ) + f ( v - 2 h ) ) z ) Γ ( 1 2 , - ( c ( v - 2 h ) + ( 2 k - u ) w + 2 ( s ( 2 k - u ) + f ( v - 2 h ) ) z ) 2 4 ( s ( 2 k - u ) + f ( v - 2 h ) ) ) + 2 ( c ( v - 2 h ) + ( 2 k - u ) w + 2 ( s ( 2 k - u ) + f ( v - 2 h ) ) z ) 2 4 ( s ( 2 k - u ) + f ( v - 2 h ) ) ( s ( 2 k - u ) + f ( v - 2 h ) ) ( - ( c ( v - 2 h ) + ( 2 k - u ) w + 2 ( s ( 2 k - u ) + f ( v - 2 h ) ) z ) 2 / ( s ( 2 k - u ) + f ( v - 2 h ) ) ) ) ) / ( ( s ( 2 k - u ) + f ( v - 2 h ) ) 2 - ( c ( v - 2 h ) + ( 2 k - u ) w + 2 ( s ( 2 k - u ) + f ( v - 2 h ) ) z ) 2 s ( 2 k - u ) + f ( v - 2 h ) ) + ( - ( c ( v - 2 h ) + ( u - 2 k ) w ) 2 4 ( s ( u - 2 k ) + f ( v - 2 h ) ) - π u 2 + t ( u - 2 k ) + g ( v - 2 h ) ( ( c ( v - 2 h ) + ( u - 2 k ) w ) ( c ( v - 2 h ) + ( u - 2 k ) w + 2 ( s ( u - 2 k ) + f ( v - 2 h ) ) z ) Γ ( 1 2 , - ( c ( v - 2 h ) + ( u - 2 k ) w + 2 ( s ( u - 2 k ) + f ( v - 2 h ) ) z ) 2 4 ( s ( u - 2 k ) + f ( v - 2 h ) ) ) + 2 ( c ( v - 2 h ) + ( u - 2 k ) w + 2 ( s ( u - 2 k ) + f ( v - 2 h ) ) z ) 2 4 ( s ( u - 2 k ) + f ( v - 2 h ) ) ( s ( u - 2 k ) + f ( v - 2 h ) ) ( - ( c ( v - 2 h ) + ( u - 2 k ) w + 2 ( s ( u - 2 k ) + f ( v - 2 h ) ) z ) 2 / ( s ( u - 2 k ) + f ( v - 2 h ) ) ) ) ) / ( ( s ( u - 2 k ) + f ( v - 2 h ) ) 2 - ( c ( v - 2 h ) + ( u - 2 k ) w + 2 ( s ( u - 2 k ) + f ( v - 2 h ) ) z ) 2 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]]]]] ( ( - ( a ( 2 k - m ) + c ( 2 h - v ) + ( 2 j - u ) w ) 2 4 ( ( 2 k - m ) p + s ( 2 j - u ) + f ( 2 h - v ) ) + ( 2 k - m ) q + t ( 2 j - u ) + π u 2 + g ( 2 h - v ) + m π 2 ( ( a ( 2 k - m ) + c ( 2 h - v ) + ( 2 j - u ) w ) ( a ( 2 k - m ) + c ( 2 h - v ) + ( 2 j - u ) w + 2 ( ( 2 k - m ) p + s ( 2 j - u ) + f ( 2 h - v ) ) z ) Γ ( 1 2 , - ( a ( 2 k - m ) + c ( 2 h - v ) + ( 2 j - u ) w + 2 ( ( 2 k - m ) p + s ( 2 j - u ) + f ( 2 h - v ) ) z ) 2 / ( 4 ( ( 2 k - m ) p + s ( 2 j - u ) + f ( 2 h - v ) ) ) ) + 2 ( a ( 2 k - m ) + c ( 2 h - v ) + ( 2 j - u ) w + 2 ( ( 2 k - m ) p + s ( 2 j - u ) + f ( 2 h - v ) ) z ) 2 4 ( ( 2 k - m ) p + s ( 2 j - u ) + f ( 2 h - v ) ) ( ( 2 k - m ) p + s ( 2 j - u ) + f ( 2 h - v ) ) ( - ( a ( 2 k - m ) + c ( 2 h - v ) + ( 2 j - u ) w + 2 ( ( 2 k - m ) p + s ( 2 j - u ) + f ( 2 h - v ) ) z ) 2 / ( ( 2 k - m ) p + s ( 2 j - u ) + f ( 2 h - v ) ) ) ) ) / ( ( ( 2 k - m ) p + s ( 2 j - u ) + f ( 2 h - v ) ) 2 ( - ( a ( 2 k - m ) + c ( 2 h - v ) + ( 2 j - u ) w + 2 ( ( 2 k - m ) p + s ( 2 j - u ) + f ( 2 h - v ) ) z ) 2 / ( ( 2 k - m ) p + s ( 2 j - u ) + f ( 2 h - v ) ) ) ) + ( - ( a ( m - 2 k ) + c ( 2 h - v ) + ( 2 j - u ) w ) 2 4 ( ( m - 2 k ) p + s ( 2 j - u ) + f ( 2 h - v ) ) + ( m - 2 k ) q + t ( 2 j - u ) + π u 2 + g ( 2 h - v ) - m π 2 ( ( a ( m - 2 k ) + c ( 2 h - v ) + ( 2 j - u ) w ) ( a ( m - 2 k ) + c ( 2 h - v ) + ( 2 j - u ) w + 2 ( ( m - 2 k ) p + s ( 2 j - u ) + f ( 2 h - v ) ) z ) Γ ( 1 2 , - ( a ( m - 2 k ) + c ( 2 h - v ) + ( 2 j - u ) w + 2 ( ( m - 2 k ) p + s ( 2 j - u ) + f ( 2 h - v ) ) z ) 2 / ( 4 ( ( m - 2 k ) p + s ( 2 j - u ) + f ( 2 h - v ) ) ) ) + 2 ( a ( m - 2 k ) + c ( 2 h - v ) + ( 2 j - u ) w + 2 ( ( m - 2 k ) p + s ( 2 j - u ) + f ( 2 h - v ) ) z ) 2 4 ( ( m - 2 k ) p + s ( 2 j - u ) + f ( 2 h - v ) ) ( ( m - 2 k ) p + s ( 2 j - u ) + f ( 2 h - v ) ) ( - ( a ( m - 2 k ) + c ( 2 h - v ) + ( 2 j - u ) w + 2 ( ( m - 2 k ) p + s ( 2 j - u ) + f ( 2 h - v ) ) z ) 2 / ( ( m - 2 k ) p + s ( 2 j - u ) + f ( 2 h - v ) ) ) ) ) / ( ( ( m - 2 k ) p + s ( 2 j - u ) + f ( 2 h - v ) ) 2 ( - ( a ( m - 2 k ) + c ( 2 h - v ) + ( 2 j - u ) w + 2 ( ( m - 2 k ) p + s ( 2 j - u ) + f ( 2 h - v ) ) z ) 2 / ( ( m - 2 k ) p + s ( 2 j - u ) + f ( 2 h - v ) ) ) ) + ( - ( a ( 2 k - m ) + c ( 2 h - v ) + ( u - 2 j ) w ) 2 4 ( ( 2 k - m ) p + s ( u - 2 j ) + f ( 2 h - v ) ) + ( 2 k - m ) q + t ( u - 2 j ) + g ( 2 h - v ) - π u 2 + m π 2 ( ( a ( 2 k - m ) + c ( 2 h - v ) + ( u - 2 j ) w ) ( a ( 2 k - m ) + c ( 2 h - v ) + ( u - 2 j ) w + 2 ( ( 2 k - m ) p + s ( u - 2 j ) + f ( 2 h - v ) ) z ) Γ ( 1 2 , - ( a ( 2 k - m ) + c ( 2 h - v ) + ( u - 2 j ) w + 2 ( ( 2 k - m ) p + s ( u - 2 j ) + f ( 2 h - v ) ) z ) 2 / ( 4 ( ( 2 k - m ) p + s ( u - 2 j ) + f ( 2 h - v ) ) ) ) + 2 ( a ( 2 k - m ) + c ( 2 h - v ) + ( u - 2 j ) w + 2 ( ( 2 k - m ) p + s ( u - 2 j ) + f ( 2 h - v ) ) z ) 2 4 ( ( 2 k - m ) p + s ( u - 2 j ) + f ( 2 h - v ) ) ( ( 2 k - m ) p + s ( u - 2 j ) + f ( 2 h - v ) ) ( - ( a ( 2 k - m ) + c ( 2 h - v ) + ( u - 2 j ) w + 2 ( ( 2 k - m ) p + s ( u - 2 j ) + f ( 2 h - v ) ) z ) 2 / ( ( 2 k - m ) p + s ( u - 2 j ) + f ( 2 h - v ) ) ) ) ) / ( ( ( 2 k - m ) p + s ( u - 2 j ) + f ( 2 h - v ) ) 2 ( - ( a ( 2 k - m ) + c ( 2 h - v ) + ( u - 2 j ) w + 2 ( ( 2 k - m ) p + s ( u - 2 j ) + f ( 2 h - v ) ) z ) 2 / ( ( 2 k - m ) p + s ( u - 2 j ) + f ( 2 h - v ) ) ) ) + ( - ( a ( m - 2 k ) + c ( 2 h - v ) + ( u - 2 j ) w ) 2 4 ( ( m - 2 k ) p + s ( u - 2 j ) + f ( 2 h - v ) ) + ( m - 2 k ) q + t ( u - 2 j ) + g ( 2 h - v ) - π u 2 - m π 2 ( ( a ( m - 2 k ) + c ( 2 h - v ) + ( u - 2 j ) w ) ( a ( m - 2 k ) + c ( 2 h - v ) + ( u - 2 j ) w + 2 ( ( m - 2 k ) p + s ( u - 2 j ) + f ( 2 h - v ) ) z ) Γ ( 1 2 , - ( a ( m - 2 k ) + c ( 2 h - v ) + ( u - 2 j ) w + 2 ( ( m - 2 k ) p + s ( u - 2 j ) + f ( 2 h - v ) ) z ) 2 / ( 4 ( ( m - 2 k ) p + s ( u - 2 j ) + f ( 2 h - v ) ) ) ) + 2 ( a ( m - 2 k ) + c ( 2 h - v ) + ( u - 2 j ) w + 2 ( ( m - 2 k ) p + s ( u - 2 j ) + f ( 2 h - v ) ) z ) 2 4 ( ( m - 2 k ) p + s ( u - 2 j ) + f ( 2 h - v ) ) ( ( m - 2 k ) p + s ( u - 2 j ) + f ( 2 h - v ) ) ( - ( a ( m - 2 k ) + c ( 2 h - v ) + ( u - 2 j ) w + 2 ( ( m - 2 k ) p + s ( u - 2 j ) + f ( 2 h - v ) ) z ) 2 / ( ( m - 2 k ) p + s ( u - 2 j ) + f ( 2 h - v ) ) ) ) ) / ( ( ( m - 2 k ) p + s ( u - 2 j ) + f ( 2 h - v ) ) 2 ( - ( a ( m - 2 k ) + c ( 2 h - v ) + ( u - 2 j ) w + 2 ( ( m - 2 k ) p + s ( u - 2 j ) + f ( 2 h - v ) ) z ) 2 / ( ( m - 2 k ) p + s ( u - 2 j ) + f ( 2 h - v ) ) ) ) + ( - ( a ( 2 k - m ) + c ( v - 2 h ) + ( 2 j - u ) w ) 2 4 ( ( 2 k - m ) p + s ( 2 j - u ) + f ( v - 2 h ) ) + ( 2 k - m ) q + t ( 2 j - u ) + π u 2 + g ( v - 2 h ) + m π 2 ( ( a ( 2 k - m ) + c ( v - 2 h ) + ( 2 j - u ) w ) ( a ( 2 k - m ) + c ( v - 2 h ) + ( 2 j - u ) w + 2 ( ( 2 k - m ) p + s ( 2 j - u ) + f ( v - 2 h ) ) z ) Γ ( 1 2 , - ( a ( 2 k - m ) + c ( v - 2 h ) + ( 2 j - u ) w + 2 ( ( 2 k - m ) p + s ( 2 j - u ) + f ( v - 2 h ) ) z ) 2 / ( 4 ( ( 2 k - m ) p + s ( 2 j - u ) + f ( v - 2 h ) ) ) ) + 2 ( a ( 2 k - m ) + c ( v - 2 h ) + ( 2 j - u ) w + 2 ( ( 2 k - m ) p + s ( 2 j - u ) + f ( v - 2 h ) ) z ) 2 4 ( ( 2 k - m ) p + s ( 2 j - u ) + f ( v - 2 h ) ) ( ( 2 k - m ) p + s ( 2 j - u ) + f ( v - 2 h ) ) ( - ( a ( 2 k - m ) + c ( v - 2 h ) + ( 2 j - u ) w + 2 ( ( 2 k - m ) p + s ( 2 j - u ) + f ( v - 2 h ) ) z ) 2 / ( ( 2 k - m ) p + s ( 2 j - u ) + f ( v - 2 h ) ) ) ) ) / ( ( ( 2 k - m ) p + s ( 2 j - u ) + f ( v - 2 h ) ) 2 ( - ( a ( 2 k - m ) + c ( v - 2 h ) + ( 2 j - u ) w + 2 ( ( 2 k - m ) p + s ( 2 j - u ) + f ( v - 2 h ) ) z ) 2 / ( ( 2 k - m ) p + s ( 2 j - u ) + f ( v - 2 h ) ) ) ) + ( - ( a ( m - 2 k ) + c ( v - 2 h ) + ( 2 j - u ) w ) 2 4 ( ( m - 2 k ) p + s ( 2 j - u ) + f ( v - 2 h ) ) + ( m - 2 k ) q + t ( 2 j - u ) + π u 2 + g ( v - 2 h ) - m π 2 ( ( a ( m - 2 k ) + c ( v - 2 h ) + ( 2 j - u ) w ) ( a ( m - 2 k ) + c ( v - 2 h ) + ( 2 j - u ) w + 2 ( ( m - 2 k ) p + s ( 2 j - u ) + f ( v - 2 h ) ) z ) Γ ( 1 2 , - ( a ( m - 2 k ) + c ( v - 2 h ) + ( 2 j - u ) w + 2 ( ( m - 2 k ) p + s ( 2 j - u ) + f ( v - 2 h ) ) z ) 2 / ( 4 ( ( m - 2 k ) p + s ( 2 j - u ) + f ( v - 2 h ) ) ) ) + 2 ( a ( m - 2 k ) + c ( v - 2 h ) + ( 2 j - u ) w + 2 ( ( m - 2 k ) p + s ( 2 j - u ) + f ( v - 2 h ) ) z ) 2 4 ( ( m - 2 k ) p + s ( 2 j - u ) + f ( v - 2 h ) ) ( ( m - 2 k ) p + s ( 2 j - u ) + f ( v - 2 h ) ) ( - ( a ( m - 2 k ) + c ( v - 2 h ) + ( 2 j - u ) w + 2 ( ( m - 2 k ) p + s ( 2 j - u ) + f ( v - 2 h ) ) z ) 2 / ( ( m - 2 k ) p + s ( 2 j - u ) + f ( v - 2 h ) ) ) ) ) / ( ( ( m - 2 k ) p + s ( 2 j - u ) + f ( v - 2 h ) ) 2 ( - ( a ( m - 2 k ) + c ( v - 2 h ) + ( 2 j - u ) w + 2 ( ( m - 2 k ) p + s ( 2 j - u ) + f ( v - 2 h ) ) z ) 2 / ( ( m - 2 k ) p + s ( 2 j - u ) + f ( v - 2 h ) ) ) ) + ( - ( a ( 2 k - m ) + c ( v - 2 h ) + ( u - 2 j ) w ) 2 4 ( ( 2 k - m ) p + s ( u - 2 j ) + f ( v - 2 h ) ) + ( 2 k - m ) q + t ( u - 2 j ) + g ( v - 2 h ) - π u 2 + m π 2 ( ( a ( 2 k - m ) + c ( v - 2 h ) + ( u - 2 j ) w ) ( a ( 2 k - m ) + c ( v - 2 h ) + ( u - 2 j ) w + 2 ( ( 2 k - m ) p + s ( u - 2 j ) + f ( v - 2 h ) ) z ) Γ ( 1 2 , - ( a ( 2 k - m ) + c ( v - 2 h ) + ( u - 2 j ) w + 2 ( ( 2 k - m ) p + s ( u - 2 j ) + f ( v - 2 h ) ) z ) 2 / ( 4 ( ( 2 k - m ) p + s ( u - 2 j ) + f ( v - 2 h ) ) ) ) + 2 ( a ( 2 k - m ) + c ( v - 2 h ) + ( u - 2 j ) w + 2 ( ( 2 k - m ) p + s ( u - 2 j ) + f ( v - 2 h ) ) z ) 2 4 ( ( 2 k - m ) p + s ( u - 2 j ) + f ( v - 2 h ) ) ( ( 2 k - m ) p + s ( u - 2 j ) + f ( v - 2 h ) ) ( - ( a ( 2 k - m ) + c ( v - 2 h ) + ( u - 2 j ) w + 2 ( ( 2 k - m ) p + s ( u - 2 j ) + f ( v - 2 h ) ) z ) 2 / ( ( 2 k - m ) p + s ( u - 2 j ) + f ( v - 2 h ) ) ) ) ) / ( ( ( 2 k - m ) p + s ( u - 2 j ) + f ( v - 2 h ) ) 2 ( - ( a ( 2 k - m ) + c ( v - 2 h ) + ( u - 2 j ) w + 2 ( ( 2 k - m ) p + s ( u - 2 j ) + f ( v - 2 h ) ) z ) 2 / ( ( 2 k - m ) p + s ( u - 2 j ) + f ( v - 2 h ) ) ) ) + ( - ( a ( m - 2 k ) + c ( v - 2 h ) + ( u - 2 j ) w ) 2 4 ( ( m - 2 k ) p + s ( u - 2 j ) + f ( v - 2 h ) ) + ( m - 2 k ) q + t ( u - 2 j ) + g ( v - 2 h ) - π u 2 - m π 2 ( ( a ( m - 2 k ) + c ( v - 2 h ) + ( u - 2 j ) w ) ( a ( m - 2 k ) + c ( v - 2 h ) + ( u - 2 j ) w + 2 ( ( m - 2 k ) p + s ( u - 2 j ) + f ( v - 2 h ) ) z ) Γ ( 1 2 , - ( a ( m - 2 k ) + c ( v - 2 h ) + ( u - 2 j ) w + 2 ( ( m - 2 k ) p + s ( u - 2 j ) + f ( v - 2 h ) ) z ) 2 / ( 4 ( ( m - 2 k ) p + s ( u - 2 j ) + f ( v - 2 h ) ) ) ) + 2 ( a ( m - 2 k ) + c ( v - 2 h ) + ( u - 2 j ) w + 2 ( ( m - 2 k ) p + s ( u - 2 j ) + f ( v - 2 h ) ) z ) 2 4 ( ( m - 2 k ) p + s ( u - 2 j ) + f ( v - 2 h ) ) ( ( m - 2 k ) p + s ( u - 2 j ) + f ( v - 2 h ) ) ( - ( a ( m - 2 k ) + c ( v - 2 h ) + ( u - 2 j ) w + 2 ( ( m - 2 k ) p + s ( u - 2 j ) + f ( v - 2 h ) ) z ) 2 / ( ( m - 2 k ) p + s ( u - 2 j ) + f ( v - 2 h ) ) ) ) ) / ( ( ( m - 2 k ) p + s ( u - 2 j ) + f ( v - 2 h ) ) 2 ( - ( a ( m - 2 k ) + c ( v - 2 h ) + ( u - 2 j ) w + 2 ( ( m - 2 k ) p + s ( u - 2 j ) + f ( v - 2 h ) ) z ) 2 / ( ( m - 2 k ) p + s ( u - 2 j ) + f ( v - 2 h ) ) ) ) ) /; m + u + v + Condition z z 1 2 a p z q m w z 1 2 s z t u z 1 2 c f z g v u 2 -1 m -1 u -1 v z Binomial m m 2 -1 Binomial u u 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`m 2 1 -1 \$CellContext`u 2 1 -1 \$CellContext`v 2 -1 u 2 -1 m -1 u -1 v -1 Binomial u u 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`u 2 1 -1 \$CellContext`v 2 k 0 m -1 2 -1 -1 k Binomial m k -1 2 k -1 m a 2 4 p -1 2 k -1 m q m 2 -1 2 -1 a 2 k -1 m 2 p z 1 2 2 k -1 m 2 4 2 k -1 m p -1 2 k -1 m a 2 k -1 m 2 p z 1 2 2 k -1 m 2 2 k -1 m p -1 1 2 p a 2 k -1 m a 2 k -1 m 2 p z 1 2 2 k -1 m Gamma 1 2 a 2 k -1 m 2 p z 1 2 2 k -1 m 2 4 2 k -1 m p -1 2 k -1 m 2 p 2 a 2 k -1 m 2 p z 1 2 2 k -1 m 2 2 k -1 m p -1 1 2 -1 -1 m -1 2 k a 2 4 p -1 m -1 2 k q -1 m 2 -1 2 -1 a m -1 2 k 2 p z 1 <