Some Combinatorial Identities some of which involving Harmonic Numbers
Some Combinatorial Identities some of which involving Harmonic Numbers
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发表时间：
2011-03
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通讯作者：
M. Kronenburg
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作者：
M. Kronenburg
证明了一个乘积差分方程，并用初等方法导出了四个组合恒等式，八个涉及广义调和数的组合恒等式和八个涉及经典调和数的组合恒等式.对于二项式系数，使用伽马函数的定义，因此也允许在恒等式中使用非整数参数。在这种情况下，广义调和数是具有复数偏移的调和数，其中经典调和数是偏移为零的特殊情况。
A product difference equation is proved and used for derivation by elementary methods of four combinatorial identities, eight combinatorial identities involving generalized harmonic numbers and eight combinatorial identities involving classical harmonic numbers. For the binomial coefficients the definition with gamma functions is used, thus also allowing non-integer arguments in the identities. The generalized harmonic numbers in this case are harmonic numbers with a complex offset, where the classical harmonic numbers are a special case with offset zero.