Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and unif...Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and uniform asymptotic expansions are got. Furthermore, the asymptotic expansions of the zeros for Krawtchouk polynomials are again deduced by using the property of the zeros of Airy function, and their corresponding error bounds axe discussed. The obtained results give the asymptotic property of Krawtchouk polynomials with their zeros, which are better than the results educed by Li and Wong.展开更多
For an odd integer n ≥ 7, this paper presented a class of n-variable rotation symmetric Boolean functions （RSBFs） with optimum algebraic immunity. The nonlinearity of the constructed functions is determined.
基金Project supported by Scientific Research Common Program of Beijing Municipal Commission of Education of China (No.KM200310015060)
文摘Krawtchouk polynomials are frequently applied in modern physics. Based on the results which were educed by Li and Wong, the asymptotic expansions of Krawtchouk polynomials are improved by using Airy function, and uniform asymptotic expansions are got. Furthermore, the asymptotic expansions of the zeros for Krawtchouk polynomials are again deduced by using the property of the zeros of Airy function, and their corresponding error bounds axe discussed. The obtained results give the asymptotic property of Krawtchouk polynomials with their zeros, which are better than the results educed by Li and Wong.
基金Supported by the National Natural Science Foundation of China ( 60603012)the Foundation of Hubei Provincial Department of Education, China (D200610004)
文摘For an odd integer n ≥ 7, this paper presented a class of n-variable rotation symmetric Boolean functions （RSBFs） with optimum algebraic immunity. The nonlinearity of the constructed functions is determined.
