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Bernoulli NumbersGenerating FunctionLocally Compact GroupStirling NumbersFinite-dimensional RepresentationBernstein PolynomialsIndex MatricesEuler PolynomialBernoulli PolynomialConvex FunctionsDifferential EquationsUmbral CalculusIndex MatrixGeneralized Hypergeometric FunctionGAMMA FunctionFrobenius-Euler PolynomialsInvariant IntegralBernoulliHypergeometric FunctionHypergeometric Series