Exact 3D Conformal Blocks from Fractional Calculus

We uncover a striking connection between conformal blocks and fractional calculus. By employing a modified form of half derivatives, we derive explicitly the exact form of the three-dimensional conformal block, expressed as the product of two hypergeometric _{4}F_{3} functions. This result provides a rigorous proof of Hogervorst's formula, conjectured nearly a decade ago. Furthermore, we demonstrate its implications for the conformal bootstrap, potentially leading to new analytical techniques and numerical tools that deepen our understanding of conformal field theory.