## Is there a closed form expression/series expansion for ∫ϵ+i∞ϵ−i∞eaz+b2z2Γ(z)Γ(1−z)dz\int_{\epsilon-i\infty}^{\epsilon+i\infty} e^{az+b^2z^2}\Gamma(z)\Gamma(1-z)dz ?

I’ve been trying to find a closed form expression/series expansion for the following integral without success: F(a,b)=∫ϵ+i∞ϵ−i∞eaz+b2z2Γ(z)Γ(1−z)dz where a,b,ϵ>0. Any input is greatly appreciated! Answer Hi dp, Using the approach I mentioned above, that is splitting the csc(πz) term into its pole part 1πz and the rest, I get an exact answer for the pole … Read more