3F2的经典变换的推广
Extensions of the Classical Transformations of 3F2
摘要：
它表明，经典的二次和三次变换的身份所满足的超几何函数${}_3F_2$可以扩展到包括额外的参数对，不同的整数。在扩展的身份，其中涉及超几何函数的任意高阶，增加的参数是非线性约束：在二次的情况下，他们是否定根的某些正交多项式的离散参数（对偶哈恩和拉卡的）。给出了推广恒等式的特殊化和应用，包括与平衡${}_7F_6(1)$级数和平衡${}_4F_3(1)$级数有关的Whipple恒等式的推广，以及其它求和恒等式的推广.
英文摘要：
It is shown that the classical quadratic and cubic transformation identities satisfied by the hypergeometric function ${}_3F_2$ can be extended to include additional parameter pairs, which differ by integers. In the extended identities, which involve hypergeometric functions of arbitrarily high order, the added parameters are nonlinearly constrained: in the quadratic case, they are the negated roots of certain orthogonal polynomials of a discrete argument (dual Hahn and Racah ones). Specializations and applications of the extended identities are given, including an extension of Whipple's identity relating very well poised ${}_7F_6(1)$ series and balanced ${}_4F_3(1)$ series, and extensions of other summation identities.
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