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differential equations, heat equation; Hermite Kampé de Fériet polynomials; Hermite polynomials; generating functions; degenerate Bernstein polynomials; degenerate Bernstein operators; degenerate Euler polynomials; variational methods; fractional Choquard equation; ground state solution; vanishing potential; positively quadratically hyponormal; quadratically hyponormal; unilateral weighted shift; recursively generated; Fubini polynomials; Euler polynomials; Bernoulli polynomials; truncated exponential polynomials; Stirling numbers of the second kind; differential equations; Bell polynomials; r-Bell polynomials; (r, β)-Bell polynomials; zeros; Möbius function; divisor functions; Euler totient function; hydraulic resistance; pipe flow friction; Colebrook equation; Colebrook–White experiment; floating-point computations; approximations; Padé polynomials; symbolic regression; orthogonal polynomials; difference-differential operator; supersymmetry; Konhauser matrix polynomial; generating matrix function; integral representation; fractional integral; degenerate Fubini polynomials; Stirling numbers