相对论性库仑积分和Zeilberger完整系统方法。I
Relativistic Coulomb Integrals and Zeilberger's Holonomic Systems Approach. I
摘要：
借助于计算机代数，我们研究了对角矩阵元<Or^p>，其中O是标准的Dirac矩阵算符，角括号表示相对论库仑问题的量子力学平均。利用Zeilberger推广的Goelberg算法及其变形，导出了每个期望值的三项递推关系，以及相应的广义超几何级数的变换公式。此外，还找到了这些积分的维里递推关系，并给出了算法证明。
英文摘要：
With the help of computer algebra we study the diagonal matrix elements <Or^p>, where O are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem. Using Zeilberger's extension of Gosper's algorithm and a variant to it, three-term recurrence relations for each of these expectation values are derived together with some transformation formulas for the corresponding generalized hypergeometric series. In addition, the virial recurrence relations for these integrals are also found and proved algorithmically.
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