On the definiteness of Gauss-Kronrod integration rules
On the definiteness of Gauss-Kronrod integration rules
The nondefiniteness of the Kronrod extension of the Gauss-Gegenbauer integration rule with weight function <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="w left-parenthesis x semicolon mu right-parenthesis equals left-parenthesis 1 minus x squared right-parenthesis Superscript mu minus 1 slash 2"> <mml:semantics> <mml:mrow> <mml:mi>w</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>x</mml:mi> <mml:mo>;</mml:mo> <mml:mi>μ<!-- μ --></mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> …