WZ方法与一类定积分的计算及其推广

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 ∫0+∞ f(t)dt=a,构造与f(t)本质上不同的函数g(t)、g(t,s)(s∈S(∈)R),使得g(t) ≡g(t,s0)(比如s0=1)且∫0+∞ g(t)dt=∫0+∞ g(t,s)dt=∫0+∞ f(t)dt=a,(...

WZ-METHOD AND CALCULATION WITH GENERALIZATION FOR A KIND OF DEFINITE INTEGRALS

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.