关于Fibonacci多项式与Lucas多项式乘积的恒等式

Some Identities on Multiplication of Fibonacci Polynomials and Lucas Polynomials

利用广义Fibonacci多项式Fn(x,y)和Lucas多项式Ln(x,y)的性质,研究组合和式Rn(x,y;tx2).结合Bernoulli和Euler多项式的生成函数,给出Fn(x,y)和Ln(x,y)的两个恒等式,进一步推广了Velasco的结果.

The summation form of Rn （x,y;tx2） is studied by the properties of generalized Fibonacci polynomials Fn （x, y） and Lucas polynomials Ln （x, y）. Meanwhile, using the generating function of Bernoulli polynomials and Euler polynomials, the two identities concerning Fn （x,y）Ln （x,y） are obtained. Thus some results obtained by Velasco are generalized.