On Fejér's inequalities for the Legendre polynomials
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DOI: 10.1002/mana.201600461
Abstract: We present various inequalities for the sum Sn(t)=∑k=0nPk(t),where Pk denotes the Legendre polynomial of degree k. Among others we prove that the inequalities 25(1+t)≤Sn(t)and3−12(1−t2)≤Sn(t)hold for all n≥1 and t∈[−1,1]. The constant factors 2/5 and (3−1)/2… read more here.
Keywords: legendre polynomials; inequalities legendre; fej inequalities;