We show that many well-known counting coefficients in combinatorics are Hamburger moment sequences in certain unified approaches and that Hamburger moment sequences are infinitely convex. We introduce the concept of t...We show that many well-known counting coefficients in combinatorics are Hamburger moment sequences in certain unified approaches and that Hamburger moment sequences are infinitely convex. We introduce the concept of the q-Hamburger moment sequence of polynomials and present some examples of such sequences of polynomials. We also suggest some problems and conjectures.展开更多
In the paper,we investigate the complete convergence and complete moment convergence for the maximal partial sum of martingale diference sequence.Especially,we get the Baum–Katz-type Theorem and Hsu–Robbins-type The...In the paper,we investigate the complete convergence and complete moment convergence for the maximal partial sum of martingale diference sequence.Especially,we get the Baum–Katz-type Theorem and Hsu–Robbins-type Theorem for martingale diference sequence.As an application,a strong law of large numbers for martingale diference sequence is obtained.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11371078)
文摘We show that many well-known counting coefficients in combinatorics are Hamburger moment sequences in certain unified approaches and that Hamburger moment sequences are infinitely convex. We introduce the concept of the q-Hamburger moment sequence of polynomials and present some examples of such sequences of polynomials. We also suggest some problems and conjectures.
基金Supported by National Natural Science Foundation of China(Grant Nos.11201001,11171001,11126176 and 11226207)Natural Science Foundation of Anhui Province(Grant Nos.1208085QA03 and 1308085QA03)+2 种基金Applied Teaching Model Curriculum of Anhui University(Grant No.XJYYXKC04)Students Innovative Training Project of Anhui University(Grant No.201310357004)Doctoral Research Start-up Funds Projects of Anhui University and the Students Science Research Training Program of Anhui University(Grant No.KYXL2012007)
文摘In the paper,we investigate the complete convergence and complete moment convergence for the maximal partial sum of martingale diference sequence.Especially,we get the Baum–Katz-type Theorem and Hsu–Robbins-type Theorem for martingale diference sequence.As an application,a strong law of large numbers for martingale diference sequence is obtained.
