• Media type: E-Article
  • Title: Saddle points of the complementary error function
  • Contributor: Fettis, Henry E.; Caslin, James C.; Cramer, Kenneth R.
  • imprint: American Mathematical Society (AMS), 1973
  • Published in: Mathematics of Computation
  • Language: English
  • DOI: 10.1090/s0025-5718-1973-0326992-9
  • ISSN: 0025-5718; 1088-6842
  • Keywords: Applied Mathematics ; Computational Mathematics ; Algebra and Number Theory
  • Origination:
  • Footnote:
  • Description: <p>The first one hundred zeros of the derivative of the function <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="w left-parenthesis z right-parenthesis equals e Superscript minus z squared Baseline upper E r f c left-parenthesis minus i z right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>w</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>e</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>−<!-- − --></mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>z</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:mrow> </mml:msup> </mml:mrow> <mml:mspace width="thickmathspace" /> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>Erfc</mml:mi> </mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mo>−<!-- − --></mml:mo> <mml:mi>i</mml:mi> <mml:mi>z</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">w(z) = {e^{ - {z^2}}}\;{\operatorname {Erfc}}( - iz)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are given, together with an asymptotic formula for estimating the higher zeros.</p>
  • Access State: Open Access