Finite order solutions of second order linear differential equations
Finite order solutions of second order linear differential equations
We consider the differential equation <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f plus upper A left-parenthesis z right-parenthesis f Superscript prime Baseline plus upper B left-parenthesis z right-parenthesis f equals 0"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>+</mml:mo> <mml:mi>A</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:msup> <mml:mi>f</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mo>+</mml:mo> <mml:mi>B</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy="false">)</mml:mo> …