ANALYTICAL SERIES EXPRESSIONS FOR HANTUSHS M-FUNCTIONS AND S-FUNCTIONS

M. S. Hantush established relationships between the dynamics of ground water mounding beneath recharge zones and two integral functions, M an d S. Exact algebraic expressions for these functions are developed in terms of a formal power series expansion. This expansion may be reorde red to provide two independent analytical partial summations involving elementary functions. The convergence characteristics of these two fo rmulae are discussed and compared with numerical quadratures of M and, hence, S. The algebraic expressions are used to generate identities f or related integrals. Compact algebraic approximations to M and S can be deduced from the series expansions with essentially arbitrary accur acy, while retaining valuable functional information. For example, a s imple two-term truncated sum yields a reasonable approximation to M ov er a useful range of arguments. The results are amenable for use in fu rther theoretical studies of groundwater percolation and mounding wher e numerical quadratures may be undesirable.