Successive derivatives of entire functions
Successive derivatives of entire functions
We show that if <italic>f</italic> is a real entire function which has, along with each of its derivatives, only real nonpositive zeros, then either <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis z right-parenthesis equals c e Superscript sigma z Baseline comma c"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> …