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The aim of this paperis to study an interpolation problem, which is an intermediate problem between Lagrange and Hermite. We consider this problem on the nodes obtained by projecting vertically the zeros ofሺ1 − ݔ ଶ ሻܲ ሺݔሻ onto the unit circle, where ܲ ሺݔሻ stands for ݊ ௧ Legendre polynomial. We prove the regularity of the problem, give explicit forms and establish a convergence theorem for the same.doi:10.22457/apam.v17n1a3 fatcat:hkef5z4ipbcnlmjv3jq6hhzbhy