Convergence of product integration rules over (0,โ) for functions with weak singularities at the origin
Convergence of product integration rules over (0,โ) for functions with weak singularities at the origin
In this paper we consider integrals of the form<disp-formula content-type="math/mathml">\[<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="integral Subscript 0 Superscript normal infinity Baseline e Superscript negative x Baseline upper K left-parenthesis x comma y right-parenthesis f left-parenthesis x right-parenthesis d x comma"><mml:semantics><mml:mrow><mml:msubsup><mml:mo>โซ<!-- โซ --></mml:mo><mml:mn>0</mml:mn><mml:mi mathvariant="normal">โ<!-- โ --></mml:mi></mml:msubsup><mml:mrow class="MJX-TeXAtom-ORD"><mml:mrow class="MJX-TeXAtom-ORD"><mml:msup><mml:mi>e</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mo>โ<!-- โ --></mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msup></mml:mrow><mml:mi>K</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>y</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo โฆ