兰州大学学报(自然科学版)
蘭州大學學報(自然科學版)
란주대학학보(자연과학판)
JOURNAL OF LANZHOU UNIVERSITY
2013年
1期
100-102
,共3页
多重Zeta值%洗牌乘积%递归
多重Zeta值%洗牌乘積%遞歸
다중Zeta치%세패승적%체귀
multiple zeta value%shuffle product%recursion
对于多重Zeta函数P n1+n2+···+nk=n n1, n2,···, nk>1(2n1,2n2,· · ·,2nk),当k=2,3,4,5时等式是已知的.利用递归的方法给出了k=6时的多重Zeta值 P n1+n2+n3+n4+n5+n6=n n1, n2, n3, n4, n5, n6>1(2n1,2n2,2n3,2n4,2n5,2n6)=231512(2n)?2164(2)(2n ?2)+21256(4)(2n ?4).
對于多重Zeta函數P n1+n2+···+nk=n n1, n2,···, nk>1(2n1,2n2,· · ·,2nk),噹k=2,3,4,5時等式是已知的.利用遞歸的方法給齣瞭k=6時的多重Zeta值 P n1+n2+n3+n4+n5+n6=n n1, n2, n3, n4, n5, n6>1(2n1,2n2,2n3,2n4,2n5,2n6)=231512(2n)?2164(2)(2n ?2)+21256(4)(2n ?4).
대우다중Zeta함수P n1+n2+···+nk=n n1, n2,···, nk>1(2n1,2n2,· · ·,2nk),당k=2,3,4,5시등식시이지적.이용체귀적방법급출료k=6시적다중Zeta치 P n1+n2+n3+n4+n5+n6=n n1, n2, n3, n4, n5, n6>1(2n1,2n2,2n3,2n4,2n5,2n6)=231512(2n)?2164(2)(2n ?2)+21256(4)(2n ?4).
@@@@Identities for the multiple zeta functionsζ(2n1, 2n2, · · · , 2nk), are known for k=2, n1+n2+···+nk=n n1, n2, ··· , nk 1 3, 4, 5. The multiple zeta values was given for k=6 by way of recursionζ(2n1, 2n2, 2n3, 2n4, 2n5, 2n6)= 231512ζ(2n)? 2164ζ(2)ζ(2n?2)+ 21256ζ(4)ζ(2n?4). n1+n2+n3+n4+n5+n6=n n1, n2, n3, n4, n5, n6 1
