一个包含Legendre多项式的积分计算问题

An integral calculating problem involving the Legendre polynomials

利用初等方法、组合方法、幂级数的惟一性以及Legendre多项式的性质,研究一个包含Legendre多项式的积分计算问题,并给出一个包含Legendre多项式的积分计算公式.

Using the elementary method,combinacial method,unique properties of the power series and the properties of the Legendre polynomials,an integral calculating problem involving the Legendre polynomials is studied.At the same time,an interesting calculating formula is given.