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Functions of bounded index, bounded value distribution and v-bounded index
Nonlinear Analysis: Theory, Methods & Applications, 1987If for an entire function f there exists an integer N such that for all \(z\in {\mathbb{C}}\) and \(k\in {\mathbb{N}}\) \[ \max_{0\leq j\leq N}\{| f^{(j)}(z)| /j!\}\geq | f^{(k)}(z)| /k!, \] then f is called of bounded index and the least number N is called the ``index'' of f.
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