The Hypergeometric Function

Notes from the “Conformal Field Theory and Operator Algebras workshop,” August 2010, Oregon. Want to relate Fμ and Gμ after analytic continuation. Writing Fμs in terms of Gνs – coefficients are ”transport coefficients.” (1) Hypergeometric function/equation (2) Compute transport coefficients for the “Basic ODE” Definition. Gauss’s hypergeometric equation: second order ODE with 3 regular singular points {0, 1,∞}: z(1− z)f ′′ + [c− (1 + a+ b)z]f ′ − abf = 0. What’s cool about this are its solutions, built from 2F1 (a, b; c; z) = Σn≥0 (a)n(b)n (c)n z n! with (a)n := a(a+ 1) · · · (a+ n− 1). Rewrite differential equation as F (z) = ( A z + B 1− z )F (z)