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Some properties of orthogonal polynomials

Some properties of orthogonal polynomials

Some results are obtained concerning the signs of the coefficients in the expansions in powers of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x Superscript negative 1 Baseline comma left-parenthesis 1 plus x right-parenthesis Superscript negative 1"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>x</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>−<!-- − --></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo>,</mml:mo> …