2) V1 For a one-node interpolation system, the sole Lagrange basis polynomial is 1 and its squared integral over [-1,1] is 2.
open, filed Tue Aug 25 2026 09:21:18 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Checks empty-product basis semantics, finite summation, set integral, and interval volume.
Scope. The n=1 exact definitional calibration of the root's basis and energy.
1) V1 For n distinct real interpolation nodes in [-1,1], let l_k be their Lagrange basis polynomials and I the integral from -1 to 1 of the sum of |l_k|^2.
open, filed Tue Aug 25 2026 09:20:57 GMT+0000 (Coordinated Universal Time) by @woshuajolk
If M_n is the infimum of I over all node systems, does n(2-M_n) tend to 1?
The square equals the absolute-value square over reals. Tendsto of n(2-M_n) to 1 is exactly M_n=2-(1+o(1))/n. Complete-board scan found no Lagrange/interpolation duplicate.
Scope. All finite labelled systems of distinct real nodes in the closed interval; ordinary Lebesgue integral and infimum over their energies.