olymmath

Putnam 1990 B2

  • Session B

Prove that for ∣x∣<1|x| < 1, ∣z∣>1|z| > 1, 1+∑j=1∞(1+xj)Pj=0,1 + \sum_{j=1}^\infty (1 + x^j)P_j = 0, where PjP_j is (1−z)(1−zx)(1−zx2)⋯(1−zxj−1)(z−x)(z−x2)(z−x3)⋯(z−xj).\frac{(1 - z)(1 - zx)(1 - zx^2) \cdots (1 - zx^{j-1})} {(z - x)(z - x^2)(z - x^3) \cdots (z - x^j)}.

Curated text Kedlaya Putnam archive. Quoted with source.

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