Geodesic
Coverings of a sphere, and extremal properties of orthogonal polynomials
Diskretnaya Matematika, Tome 7 (1995) no. 3, pp. 81-88

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We present a method of covering a multidimensional sphere by spherical caps based on spherical designs. The following extremal problem is solved: for which greatest $\eta$ a polynomial over the Gegenbauer system with the zero coefficient equal to $0$ is non-negative on $[-1;\eta]$? 
@article{DM_1995_7_3_a7,
     author = {V. A. Yudin},
     title = {Coverings of a sphere, and extremal properties of orthogonal polynomials},
     journal = {Diskretnaya Matematika},
     pages = {81--88},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1995_7_3_a7/}
}
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V. A. Yudin. Coverings of a sphere, and extremal properties of orthogonal polynomials. Diskretnaya Matematika, Tome 7 (1995) no. 3, pp. 81-88. http://geodesic.mathdoc.fr/item/DM_1995_7_3_a7/