Abstract
A sufficient conditions for the nodes xi (where X0 < x1 < … < xn) and for the numbers yi (i = 0, 1..., n) and J’0 for which a polynomial spline function s of degree k+1 (k ≥ 1) interpolating the data yi in nodes xi and such that s’(x0) = y’0 sϵCk [x0,xn] are given. An explicit form for the spline function s are given.
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