Polynomial Sequences and Their Applications

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polyexponential function; Fubini polynomials; poly-Fubini polynomials; unipoly function; Stirling numbers; formal power series; composition of generation functions; bivariate generating function; composita; explicit formula; orthogonal polynomials; Meixner; perturbed Meixner–Pollaczek; moments; recurrence coefficients; difference equations; differential equations; zeros; Polynomial sequences; Appell polynomials; bivariate Appell sequence; orthogonal polynomials; extrapolation methods; Padé approximation; continued fractions; rational interpolation; complex analysis; software; abstract algebra; Jacobi polynomials; generalized hypergeometric functions; Chebyshev polynomials; linearization coefficients; connection formulas; moments formulas; symbolic computation; Riccati differential equation; tau method; polynomial computability; p-computability; Gandy’s fixed point theorem; semantic programming; polynomial operators; ${\Delta }_0^p$; computer science; block cyclic reduction; block tridiagonal matrix; characteristic polynomial; linear system; Chebyshev polynomials; Chebyshev interpolation operator; the Legendre norm; Legendre–Chebyshev spectral method; Clenshaw–Curtis quadrature; multidomain; multi-dimensions; polynomiality; polynomial function; polynomial algorithm; Turing machine; logical programming language; semantic programming; smart contract; blockchain; AI; ordinary differential equations; fractional differential equations; multistep methods; collocation; convergence; stability; polynomial sequences; central factorial polynomials; odd and even polynomials; discrete operators; Hessenberg determinant; recurrence; weighted ℬ-statistical convergence; shape parameter α; shape parameter λ; blending-type operators; computer graphics; extended dynamic mode decomposition; Koopman operator; orthogonal polynomials; mathematical modeling; dynamic systems; sheffer sequence; recurrence relation; polynomial sequences; generating functions; umbral calculus; n/a