楊倩麗,劉欣宇

(渭南師范學(xué)院數(shù)學(xué)與信息科學(xué)系,陜西渭南 714000)

關(guān)于勒讓德多項式與契貝謝夫多項式間的關(guān)系

楊倩麗,劉欣宇

(渭南師范學(xué)院數(shù)學(xué)與信息科學(xué)系,陜西渭南 714000)

主要研究勒讓德多項式與契貝謝夫多項式之間的關(guān)系的性質(zhì),利用生成函數(shù)和函數(shù)級數(shù)展開的方法,得出了勒讓德多項式與契貝謝夫多項式之間的一個重要關(guān)系,這對勒讓德多項式與契貝謝夫多項式的研究有一定的推動作用.

勒讓德多項式;恒等式;契貝謝夫多項式

1 引言及主要結(jié)論

的系數(shù)定義的,它們在函數(shù)的正交性理論研究中占有十分重要的位置,并引起了不少學(xué)者的重視和興趣,文[1-4]利用此理論給出了Fibonacci數(shù)的一些性質(zhì).本文得到勒讓德多項式與契貝謝夫多項式之間的一個重要關(guān)系．

2 幾個引理

3 定理的證明

于是完成了定理的證明.

[1]Zhang Wenpeng.Some identities involving the Fibonacci numbers[J].The Fibonacci Quarterly,1997,35:225-229.

[2]Li Hailong.On generalized Euler constants and an integral related to the Piltz divisor problem[J].Proc.Sci. Sem.Fac.Phys.Math.Siauliai Univ.,2005,8:81-89.

[3]Li Hailong,Toda M.Elaboration of some results of Srivastava and Choi[J].Journal of Analysis and Application,2006,25:517-533.

[4]Li Hailong,Kanemitus S.Tsukada H.Modular relation interpretation of the series involving the Riemann zeta values[J].Proceedings of The Japan Academy Series A:Mathematical Sciences,2008,84(8):133-162.

[5]周亞蘭,王霞.勒讓德多項式的性質(zhì)與契貝謝夫多項式間的關(guān)系[J].純粹數(shù)學(xué)與應(yīng)用數(shù)學(xué),1999,15(4):75-81.

On relationship of Legendre polynomials and Chebyshev polynomials

YANG Qian-li,LIU Xin-yu
(Department of Mathematics and Information Science, Weinan Teachers University,Weinan714000,China)

This paper discusses a property of the Legendre polynomials and Chebyshev polynomials,by a means of form faction and function series,an important relationship of the Legendre polynomials and Chebyshev polynomials is given.It will have a certain impetus to the research of the Legendre polynomials and Chebyshev polynomials.

Legendre polynomials,identity,Chebyshev polynomials

O156.4

A

1008-5513(2009)03-0448-06

2007-11-10.

陜西省自然科學(xué)基金(SJ08A22).

楊倩麗(1964-),教授,研究方向：數(shù)論.

2000MSC:11B83