MatrixProductIntegral.m

Block[{α, β, γ, δ, ε, ζ, η, θ, κ, λ, μ, ν, ξ, 𝒟 = ParabolicCylinderD},
      α = -((I (b^2 - 4 a (c + I √a)))/(8 a^(3/2))); 
      β = -(((1/2 - I/2) b)/a^(3/4)); 
      γ = (I (-(4 c a) + b^2 + 4 I a^(3/2)))/(8 a^(3/2)); 
      δ = ((1/2 + I/2) b)/a^(3/4); 
      ε = (-(4 I c a) + I b^2 + 4 a^(3/2))/(8 a^(3/2)); 
      ζ = b 𝒟[γ, δ] - (1 - I) a^(3/4) 𝒟[ε, δ]; 
      η = (4 I c a - I b^2 + 4 a^(3/2))/(8 a^(3/2)); 
      θ = 1/(2 ζ 𝒟[α, β] + (2 + 2 I) a^(3/4) 𝒟[η, β] 𝒟[γ, δ]); 
      ξ = ((1/2 + I/2) (b + 2 a))/a^(3/4); 
      κ = -(((1/2 - I/2) (b + 2 a))/a^(3/4)); 
      λ = (b + 2 a) 𝒟[γ, ξ] - (2 - 2 I) a^(3/4) 𝒟[ε, ξ]; 
      μ = b 𝒟[γ, δ] - (2 - 2 I) a^(3/4) 𝒟[ε, δ]; 
      ν = 𝒟[-((I (b^2 - 4 I a^(3/2) - 4 c a))/(8 a^(3/2))), β]; 
      {{θ (λ ν + 𝒟[γ, δ] ((b + 2 a) 𝒟[α, κ] + (2 + 2 I) a^(3/4) 𝒟[η, κ])), 
        (I √a (𝒟[α, β] 𝒟[γ, ξ] - 𝒟[α, κ] 𝒟[γ, δ]))/(ζ 𝒟[α, β] + (1 + I) a^(3/4) 𝒟[η, β] 𝒟[γ, δ])}, 
       {(I θ (μ (b + 2 a) 𝒟[α, κ] - b λ 𝒟[α, β] - (2 + 2 I) a^(3/4) (λ 𝒟[η, β] - μ 𝒟[η, κ])))/(2 √a), 
        θ (μ 𝒟[α, κ] + 𝒟[γ, ξ] (b ν + (2 + 2 I) a^(3/4) 𝒟[η, β]))}}]