Combinatorial Identities and Inequalities for Trigonometric Sums

Horst Alzer (), Omran Kouba () and Man Kam Kwong ()
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Omran Kouba: Higher Institute for Applied Sciences and Technology
Man Kam Kwong: The Hong Kong Polytechnic University

A chapter in Discrete Mathematics and Applications, 2020, pp 7-33 from Springer

Abstract: Abstract The purpose of this paper is twofold. 1. We present two short and elementary new proofs for the identity ( ∗ ) ∑ k = 0 n n k c k + m ( z + 1 ) k = ∑ k = 0 n n k n − k + c n + m z k , $$\displaystyle {(*)} \quad \sum _{k=0}^n {n\choose k}{c\choose k+m} (z+1)^k = \sum _{k=0}^n {n\choose k}{n-k+c\choose n+m} z^k, $$ which was recently proved by Chen and Reidys by using combinatorial methods. 2. Inspired by (∗) we obtain identities and inequalities for certain trigonometric sums. Among others, we show that the inequality 0

Keywords: Combinatorial identities; Trigonometric sums; Inequalities; Harmonic numbers; Vandermonde convolution formula; Legendre polynomials; 05A19; 26D05; 33B15; 33C45 (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-030-55857-4_2

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DOI: 10.1007/978-3-030-55857-4_2

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