二项式系数级数连带奇数倒数平方和
The Binomial Coefficient Series Is Associated with a Sum of Odd Reciprocal Squares
摘要:
根据一个已知级数，使用裂项方法得到分母含奇偶性不定因子 1个，2个，3个，4个，5个线性因子的二项式系数级数连带奇数倒数平方和。利用反正弦与反双曲正弦关系给出交错二项式系数级数连带奇数倒数平方和。所给出级数的和式是封闭形的。并给出二项式系数级数连带奇数倒数平方和数值恒等式。
Abstract:
Using one known series, we can structure several new binomial coefficient series which is associated with a sum of odd reciprocal squares. Their denominator has parity indefinite linear factors 1, 2, 3, 4, 5. Using relation of inverse Trigonometric and Hyperbolic function, we get that alternating the binomial coefficient series is associated with a sum of odd reciprocal squares. The numerical identities of binomial coefficient series with odd reciprocal square are given.
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