从h指数、g指数和e指数的定义出发，通过数学推导和实例验证给出g指数与h指数、e指数的不等式关系和函数关系表达式；通过对文献检索数据的统计分析，总结出论文按引频大小递减排序时，引频数随论文序号的变化规律的数学表达式；通过实例计算和比较，证实g指数对引频数非常敏感，并对这种敏感性的根源进行分析。最后对如何利用g指数客观评价科技工作者学术水平的问题进行探讨。
Based on the definition of h, g and e indexes, an inequality and a formula of the functional relation among them are established by mathematical derivations and confirmed by data of literature search. By statistical analysis of the data of literature search, a mathematical equation regarding cited times as a function of sort order of papers is given when they are arranged in the descending order of their number of citations. By comparison of the indexes calculated with the data of the literature search, it is confirmed that the g is very sensitive to the number of citations, and the origin of such sensitivity is also analyzed. A discussion on how to use the g index to evaluate academic level of a scholar is also presented.
[1] Hirsch J E. An index to quantify an individual's research output[J].Proceedings of National Academy of Sciences, 2005, 102(46):16569-16572.
[2] Bartneck C, Kokkelmans S. Detecting h-index manipulation through self-citation analysis[J].Scientometrics, 2011, 87(1):85-98.
[3] Hirsch J E. An index to quantify an individual's scientific research output that takes into account the effect of multiple coauthorship[J].Scientometrics, 2010, 85(3):741-754.
[4] 马妍, 何苗, 邢星, 等. H指数与类H指数应用于人才遴选的可行性探讨[J]. 情报科学, 2013, 31(6): 60-66.
[5] 刘合艳, 房俊民, 苑彬成. h指数研究及应用概述[J]. 情报理论与实践, 2009, 32(11):1-5.
[6] 张垒, 唐恒. 影响h指数、g指数、影响因子因素的相关性研究[J].图书情报工作, 2009, 53(20):139-143.
[7] Egghe L.An improvement of the h-index:The g-index[J]. ISSI Newsletter, 2006, 2(1):8-9.
[8] Zhang Chunting.The e-index, complementing the h-index for excess citations[J].PLoS ONE, 2009, 4(5): 1-4.
[9] Egghe L. Theory and practice of the g-index[J]. Scientometrics, 2006, 69: 131-135.
