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We study the renormalization group flow for the Higgs self coupling in thepresence of gravitational correction terms. We show that the resulting equationis equivalent to a singular linear ODE, which has explicit solutions in termsof hypergeometric functions. We discuss the implications of this model withgravitational corrections on the Higgs mass estimates in particle physicsmodels based on the spectral action functional.

Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models