Use of the generating function to generalize the sum formula for quadruple zeta values
arXiv:1503.01194
Abstract
In the present paper, we prove an identity for the generating function of the quadruple zeta values. Taking homogeneous parts on both sides of the identity and substituting appropriate values for the variables, we obtain the sum formula for quadruple zeta values. We also obtain its weighted analogues, which include the formulas for this case proved by Guo and Xie (2009, J. Number Theory 129, 2747--2765) and by Ong, Eie, and Liaw (2013, Int. J. Number Theory 9, 1185--1198).
Ver.3: I have changed the inverse into the transpose in matrix action, and modified overall sentences for readability. The main results are not changed