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A transplantation theorem for ultraspherical coefficients
Let f(θ) be integrable on (0, π) and define a n = [' f(β) cos nθ dθ , K = « 1/2 ί* /(<?)P»(cos 0)(sin θγ'HΘ Jo Jo where P n (x) is the Legendre polynomial of degree n.Then (1) c ^ ±\a n \Kn + for 1 < p …