Some Positive Trigonometric Sums
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Publication:5655819
DOI10.2307/1997054zbMath0244.42002OpenAlexW4230111467MaRDI QIDQ5655819
Publication date: 1974
Full work available at URL: https://doi.org/10.2307/1997054
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Inequalities for trigonometric functions and polynomials (26D05) Trigonometric polynomials, inequalities, extremal problems (42A05) Exponential and trigonometric functions (33B10)
Related Items (34)
A note on convergence of Newton interpolating polynomials ⋮ Coefficients of trigonometric series with nonnegative partial sums ⋮ An extension of Vietoris's inequalities ⋮ Hypercomplex polynomials, Vietoris' rational numbers and a related integer numbers sequence ⋮ Positivity of Cotes numbers at more Jacobi abscissas ⋮ Location of the zeros of certain parametric families of functions of generalized Fresnel integral type ⋮ On the stability of explicit finite difference methods for advection–diffusion equations ⋮ Coefficient conditions for starlikeness of nonnegative order ⋮ ROOTS OF TRIGONOMETRIC POLYNOMIALS AND THE ERDŐS–TURÁN THEOREM ⋮ On the positivity of certain trigonometric sums and their applications ⋮ Positivity and boundedness of trigonometric sums ⋮ Stable functions and Vietoris' theorem ⋮ An improved Vietoris sine inequality ⋮ On the study of trigonometric polynomials using strum sequence ⋮ Classes of Nonnegative Sine Polynomials ⋮ Piecewise trigonometric Hermite interpolation ⋮ On a conjecture for trigonometric sums and starlike functions ⋮ On a cosine polynomial of Turán and its sine counterpart ⋮ Extensions of Vietoris's inequalities I ⋮ Stable functions and extension of Vietoris' theorem ⋮ On the Fourier transform of the symmetric decreasing rearrangements ⋮ On a conjecture for trigonometric sums and starlike functions. II. ⋮ High precision computation of a constant in the theory of trigonometric series ⋮ A refinement of Vietoris' inequality for sine polynomials ⋮ Rational extension of the Newton diagram for the positivity of \({}_1F_2\) hypergeometric functions and Askey-Szegö problem ⋮ On two trigonometric inequalities of Askey and Steinig ⋮ Analysis of the spectral symbol associated to discretization schemes of linear self-adjoint differential operators ⋮ Inequalities for sine sums with more variables ⋮ A note on Vietoris' number sequence ⋮ On generalized Vietoris' number sequences ⋮ On the positivity of certain Cotes numbers ⋮ Further improvements of Askey-Steinig’s inequalities for finite sums involving sine and cosine ⋮ A class of positive trigonometric sums ⋮ Problems which interest and/or annoy me
Cites Work
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- On a monotonicity property of Bessel functions
- Positive Jacobi polynomial sums
- Positivity of the Cotes numbers for some Jacobi abscissas
- On the positivity of certain sums of ultraspherical polynomials
- Positivity of the Cotes Numbers for Some Ultraspherical Abscissas
- Some Monotonicity Properties of Bessel Functions
- The Sign of Lommel's Function
- Some Absolutely Monotonic and Completely Monotonic Functions
- Inequalities for the Zeros of Legendre Polynomials and Related Functions
- On a monotonic property of certain Sturm-Liouville functions
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