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- W2000003849 abstract "We prove that the inequalities ∑ k = 1 n sin ( k x ) k + 1 ≥ 1 384 ( 9 − 137 ) 110 − 6 137 = − 0.044419686 . . . and ∑ k = 1 n sin ( k x ) + cos ( k x ) k + 1 ≥ − 1 2 are valid for all real numbers x ∈ [ 0 , π ] and all positive integers n . The constant lower bounds are sharp. Our theorems complement a classical result of Rogosinski and Szegö, who proved in 1928 that the inequality ∑ k = 1 n cos ( k x ) k + 1 ≥ − 1 2 holds for all x ∈ [ 0 , π ] and n ≥ 1 ." @default.
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- W2000003849 date "2015-02-01" @default.
- W2000003849 modified "2023-09-29" @default.
- W2000003849 title "Rogosinski–Szegö type inequalities for trigonometric sums" @default.
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- W2000003849 doi "https://doi.org/10.1016/j.jat.2014.04.007" @default.
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