Roots of ๐ฝแตง(๐ง)ยฑ๐๐ฝแตงโโ(๐ง)=0 and the evaluation of integrals with cylindrical function kernels
Roots of ๐ฝแตง(๐ง)ยฑ๐๐ฝแตงโโ(๐ง)=0 and the evaluation of integrals with cylindrical function kernels
An elementary proof is presented showing that the function <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 upper J Subscript gamma Baseline left-parenthesis z right-parenthesis plus-or-minus i upper J Subscript gamma plus 1 Baseline left-parenthesis z right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mspace linebreak="newline"/> <mml:mrow โฆ