Mei Bai, Wenchang Chu
Abstract
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Five binomial sums are extended by a free parameter m , that are shown, through the generating function method, to have the same value. These sums generalize the ones by Ruehr (1980), who discovered them in the study of two unexpected equalities between definite integrals.
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Five binomial sums are extended by a free parameter m , that are shown, through the generating function method, to have the same value. These sums generalize the ones by Ruehr (1980), who discovered them in the study of two unexpected equalities between definite integrals.
Key concepts: Mathematics, Binomial coefficient, Binomial (polynomial), Central binomial coefficient, Binomial theorem, Generating function, Value (mathematics), Function (biology)