Geodesic
Positive-definite splines of special form
Sbornik. Mathematics, Tome 193 (2002) no. 12, pp. 1771-1800 Cet article a éte moissonné depuis la source Math-Net.Ru

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Even positive-definite splines with support in $[-1,1]$ that are equal to real algebraic polynomials on $[0,1]$ are investigated. Examples of such splines are presented. Under consideration are the $e$-splines, which have several extremal properties, and the positive-definite $A$-splines, which have the maximum possible smoothness on $\mathbb R$. An estimate of the approximation by a linear combination of shifts of an $A$-spline is indicated. New relations for the hypergeometric function ${_1F_2}$ are found. 
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V. P. Zastavnyi; R. M. Trigub. Positive-definite splines of special form. Sbornik. Mathematics, Tome 193 (2002) no. 12, pp. 1771-1800. http://geodesic.mathdoc.fr/item/SM_2002_193_12_a2/

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