Polynomials defined by generating relations
Polynomials defined by generating relations
Various authors have made efforts for finding new generating functions for known polynomial sets. In the present paper, by making use of the operator<inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T Subscript k Baseline equals x left-parenthesis k plus x upper D right-parenthesis"><mml:semantics><mml:mrow><mml:mrow class="MJX-TeXAtom-ORD"><mml:msub><mml:mi>T</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:mrow><mml:mo>=</mml:mo><mml:mi>x</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mi>x</mml:mi><mml:mi>D</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:annotation encoding="application/x-tex">{T_k} = x(k + xD)</mml:annotation></mml:semantics></mml:math></inline-formula>, a number …