【摘要】 勒让德多项式P_l(x)具有在边界x=1处的函数值等于1的重要性质.针对这个性质的证明，大部分数学物理方法教材借助勒让德多项式的微分公式、积分表达式或者勒让德多项式的生成函数给与证明.本文拟直接从勒让德多项式的定义出发，结合组合数的求和公式，证明这一性质.更多还原

【Abstract】 Legendre polynomials have the important property that the function value at the boundary x=1 is equal to 1. For the proof of this property, most mathematical physics books use the integral expression, differential formula, or generation function of Legendre polynomials. This paper intends to prove it directly from the definition of Legendre polynomials, combined with the summation formula of combinatorial numbers.更多还原