We study the renormalization group flow for the Higgs self coupling in the
presence of gravitational correction terms. We show that the resulting equation
is equivalent to a singular linear ODE, which has explicit solutions in terms
of hypergeometric functions. We discuss the implications of this model with
gravitational corrections on the Higgs mass estimates in particle physics
models based on the spectral action functional.Comment: 25 pages, LaTeX, 8 PDF figure