Bounding the intersection number c₂ of a distance-regular graph with classical parameters (D,b,α,β) in terms of b

Let Γ be a distance-regular graph with classical parameters (D,b,α,β) and b≥1. It is known that Γ is Q-polynomial with respect to θ₁, where θ₁=[Formula presented]−1 is the second largest eigenvalue of Γ. And it was shown that for a distance-regular graph Γ with classical parameters (D,b,α,β), D≥5 and b≥1, if a₁ is large enough compared to b and Γ is thin, then the intersection number c₂ of Γ is bounded above by a function of b. In this paper, we obtain a similar result without the assumption that the graph Γ is thin.