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1. Let 
be an analytic function with radius of convergence R (0 < R < ∞). Set
and let the order p and lower order ⋋ of f(z) be defined by
where x = Rr/(R — r). If 0 < ᑭ < ∞, we define the type T and lower type t of f(z) by
Also, if 0 < ᑭ < ∞, define the “growth numbers” 𝛄 and δ by
The purpose of our discussion will be to obtain some inequalities involving the growth constants defined above.
