The analytical calculation of the area moments of inertia used for special mechanical tests in materials science and further generalizations for moments of different orders and broader symmetry properties has led to a...The analytical calculation of the area moments of inertia used for special mechanical tests in materials science and further generalizations for moments of different orders and broader symmetry properties has led to a new type of trigonometric power sums. The corresponding generalized equations are presented, proven, and their characteristics discussed. Although the power sums have a basic form, their results have quite different properties, dependent on the values of the free parameters used. From these equations, a large variety of power reduction formulas can be derived. This is shown by some examples.展开更多
设Tn(x),Un(x)是Chebyshev多项式,复数d≠0,利用发生函数方法给Chebyshev多项式方幂和sum from k=1 to n U_k^r dk,sum from k=0 to n T_k^r dk计算公式,并进一步得到方幂和sum from k=1 to n U_k^r sin ka,sum from k=0 to n T_k^r sin...设Tn(x),Un(x)是Chebyshev多项式,复数d≠0,利用发生函数方法给Chebyshev多项式方幂和sum from k=1 to n U_k^r dk,sum from k=0 to n T_k^r dk计算公式,并进一步得到方幂和sum from k=1 to n U_k^r sin ka,sum from k=0 to n T_k^r sin ka计算公式,展开更多
文摘The analytical calculation of the area moments of inertia used for special mechanical tests in materials science and further generalizations for moments of different orders and broader symmetry properties has led to a new type of trigonometric power sums. The corresponding generalized equations are presented, proven, and their characteristics discussed. Although the power sums have a basic form, their results have quite different properties, dependent on the values of the free parameters used. From these equations, a large variety of power reduction formulas can be derived. This is shown by some examples.
文摘设Tn(x),Un(x)是Chebyshev多项式,复数d≠0,利用发生函数方法给Chebyshev多项式方幂和sum from k=1 to n U_k^r dk,sum from k=0 to n T_k^r dk计算公式,并进一步得到方幂和sum from k=1 to n U_k^r sin ka,sum from k=0 to n T_k^r sin ka计算公式,
