| 关于厄密多项式与抛物线柱函数的积和式 |
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| 引用本文： | 王念良,赵健.关于厄密多项式与抛物线柱函数的积和式[J].商洛学院学报,2007,21(2):11-13. |
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| 作者姓名： | 王念良 赵健 |
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| 作者单位： | 商洛学院数学研究所、数学系,陕西商洛,726000 |
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| 基金项目： | 国家自然科学基金;陕西省科研项目;商洛学院校科研和教改项目 |
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| 摘 要： | 目的研究厄密多项式与抛物线柱函数线性组合的性质.方法初等数论的方法和解析数论的方法.结果给出了一类关于厄密多项式Hn（x）与抛物线柱函数Dn（x）线性组合的恒等式.结论厄密多项式Hn（x）与抛物线柱函数Dn（x）是量子力学、数值逼近、函数论中两个重要的特殊函数,因此所得恒等式将对抛物线柱函数在量子力学、数值逼近的应用起到积极的作用.
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| 关 键 词： | 厄密多项式 抛物线柱函数 恒等式 积和式 |
| 文章编号： | 1674-0033（2007）02-0011-03 |
| 修稿时间： | 2007-01-05 |
Sum of Products Involving Hermite Polynomials and Parabolic Cylinder Function |
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| WANG Nian-liang,ZHAO Jian.Sum of Products Involving Hermite Polynomials and Parabolic Cylinder Function[J].Journal of Shangluo University,2007,21(2):11-13. |
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| Authors: | WANG Nian-liang ZHAO Jian |
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| Institution: | Department of Mathematics,Institute of Mathematice,Shangluo University,Shangluo,Shaanxi 726000 |
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| Abstract: | Aim To study the linear combination properties of polynomials and parabolic cylinder function.Methods Methods of Elementary Number Theory and analytic Number Theory.Results Obtained some linear combination identities involving Hermite polynomials and parabolic cylinder function.Conclusion polynomials and parabolic cylinder function are two important special functions in the fields of Quantum Mechanics,Digital Approximation and Theory of Functions.The identities we obtained in this paper will play an active role in the applications of Quantum Mechanics and Digital Approximation. |
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| Keywords: | Hermite polynomials parabolic cylinder function identities sum of product |
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