AI 中文总结
该研究推导含双伽马函数的有穷与无穷级数的变换及求和公式，通过广义超几何函数对偶关系取极限等方法得到结果，部分恒等式可消去双伽马项，仅保留超几何函数乘积形式。
AI 中文摘要
我们推导了涉及双伽马函数的有穷级数与无穷级数的变换公式及求和公式。主要结果通过对广义超几何函数的对偶关系及其推论取极限得到。部分公式通过欧拉变换的参数微分及相邻关系进一步拓展。多数恒等式将超几何级数与双伽马级数的乘积表示为超几何函数，部分有穷双伽马和的计算涉及伯努利多项式，若干情形下双伽马项抵消，得到仅含超几何函数乘积的恒等式。
英文摘要
We derive transformation and summation formulas for terminating and nonterminating series involving the digamma function. Our principal results are obtained by a limiting process starting with duality relations for the generalized hypergeometric functions and their consequences. Selected formulas are further extended by parameter differentiation of Euler's transformation and by using contiguous relations. Most of our identities express products of hypergeometric and digamma series in terms of hypergeometric functions, and some evaluations of terminating digamma sums involve Bernoulli polynomials. In several cases the digamma contributions cancel, producing identities involving only products of hypergeometric functions.
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