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The following notion of bounded index for complex entire functions was presented by Lepson. function  f ( z ) is of bounded index if there exists an integer  N  independent of  z , such thatmax   {  l  :  0  ≤  l  ≤  N  }|f   (  l  )    (  z  )    |l  !≥|f   (  n  )    (  z  )    |n  !for alln  .    $$ \max\limits_{\{l: 0\leq l\leq N\}} \left \{ \frac{|{f^{(l)}(z)}|}{l!}\right \} \geq \frac{|{f^{(n)}(z)}|}{n!}\quad\text{for all}\,\, n. $$

A characterization of holomorphic bivariate functions of bounded index