The reciprocal of an entire function of infinite order and the distribution of the zeros of its second derivative
The reciprocal of an entire function of infinite order and the distribution of the zeros of its second derivative
Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f"> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding="application/x-tex">f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a real entire function of infinite order whose zeros together with those of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="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> </inline-formula> are all real. It is proved that …