2015/10/17 by Wolfgang Gabcke, Gabcke, Wolfgang
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA
paper · pdf · doi:10.48550/arxiv.1510.06282
arxiv created 2015/10/17 · arxiv updated 2015/10/22
We prove that the Fourier cosine series ∑k=1∞(-1)k+1\fracrkcoskϕk+2 assumes its maximum value at ϕ= 0 for ϕ∈ [0, π) regardless of r if r ∈ (0, 1]. This was first proved by Arias de Reyna and van de Lune. The more compact proof presented here is based on a generating function of the Chebyshev Polynomials.