Real zeros of derivatives of meromorphic functions and solutions of second order differential equations
Real zeros of derivatives of meromorphic functions and solutions of second order differential equations
We classify all functions <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F"> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding="application/x-tex">F</mml:annotation> </mml:semantics> </mml:math> </inline-formula> meromorphic in the plane with only real zeros and real poles which satisfy the additional conditions that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper F prime"> <mml:semantics> <mml:msup> <mml:mi>F</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:annotation encoding="application/x-tex">F’</mml:annotation> </mml:semantics> </mml:math> …