Kartik Prabhu replied to a post on Twitter with Mathematica tells me the integrals are supposed to be 2 π^(1/2) Γ(1 +1/m)/Γ(1/2+1/m) for Re(m) > 0. That can be analytically continued. Send me the link to your response (Learn more) Send Likes Leo C. Stein 🦁 on Twitter