Combinatorics and flexure (Q1092702)

(From authors' summary.) Combinatorial identities, trigonometric formulas, together with complex variable techniques are used to derive exact and closed expressions for the six flexure functions of certain isotropic cylinders under flexure. The cross sections are bounded either by the closed curves \(r=\alpha \cos^ n(\theta /n)\) \((-\pi <\theta \leq \pi)\) or the closed curves \(r=\alpha | \sin (\theta /n)|^ n\) \((-\pi <\theta \leq \pi)\), where n is a positive integer \((n>1)\).