Beta-Gamma函数对余元公式的推导与实现

Realization and Demonstration of Odd Element Formula by Beta-Gamma Function

对构造的公式①,在复数域将其被积函数分解得2n个复根.在实数域将其实虚部积分取极限获证.对构造的公式②,由①将其被积函数的连续性、收敛性及一致收敛性与构造的有理数列用变量替换代入取极限获证.再由①与②应用Gamma-Beta函数的另一形式及(3),得到了余元公式的实现.

For constructed formula（1）, and make integrand（formula）in complex field decompose into 2n times complexroots,and make real and imaginary part in real number field integrate and then obtain the limit, presenting constructed formula（2）. And make the continuity, astringency, uniform convergence and constructed rational line of integrand（ formula） from the result （1） arrange firstly into various variable quantities, replace and substitute each one. Secondly, obtain the limit. Another way from the result（1）,（2）each applied into Gamma-Beta Function,and obtain the realization of Odd Element Formula by using another way and the result（3）.