A series expansion for the first positive zero of the Bessel functions
A series expansion for the first positive zero of the Bessel functions
It is shown that the first positive zero <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="j Subscript v comma l"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>j</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>v</mml:mi> <mml:mo>,</mml:mo> <mml:mi>l</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{j_{v,l}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of the Bessel function <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper J Subscript v Baseline left-parenthesis x …