摘要:
结合WZ理论中的有关结果与留数定理,借助计算机代数系统给出了下列问题的一种解答:已知 ,构造与f(t)本质上不同的函数g(t)、g(t,s) (sS ),使得g(t)=g(t,s) (比如s=1 )且 , ,由此得到了一些新的积分公式,给出了某些已知积分公式的新的简洁的证明,并将其推广.特别地,由此方法重新获得了Cadwell于1947年利用围道积分建立的下列等式: ,而且还给出了它的一个推广.
Abstract:
By the related results of WZ theory and the residue theorem,with the help of computer algebraic system,a kind of solution for the following problem are obtained:for any given ,how to construct functions g(t)、g(t,s) (where sS R ),different from f(t) in essence ,so that g(t)=g(t,s) (e.g. s=1 )and , . From the above result, either some new integral formulas or a simple but new proof for some known integral formulas can be found and generalized.In particular,the identity is proved and generalized,which wad obtained by Cadwell in 1947 by using contour integration.
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