Celebratio Mathematica — Askey — Complete Bibliography

Complete Bibliography

Works connected to John Steinig

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R. Askey and J. Steinig: “Some positive trigonometric sums,” Trans. Am. Math. Soc. 187 (1974), pp. 295–307. MR 338481 Zbl 0244.42002 article

Vietoris found an interesting generalization of the classical inequality \[ \sum_{k=1}^n\frac{\sin k\theta}k > 0 ,\] \( 0 < \theta < \pi \). A simplified proof is given for his inequality and his similar inequality for cosine series. Various new results which follow from these inequalities include improved estimates for the location of the zeros of a class of trigonometric polynomials and new positive sums of ultraspherical polynomials which extend an old inequality of Fejér. Both of Vietoris’ inequalities are special cases of a general problem for Jacobi polynomials, and a summary is given of known results on this problem.

R. Askey and J. Steinig: “A monotonic trigonometric sum,” Am. J. Math. 98 : 2 (1976), pp. 357–365. MR 407513 Zbl 0334.42003 article