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Comment on “Evaluation of the Hantush's M ( α , β ) function using binomial coefficients” by B. A. Mamedov and A. S. Ekenoğlu
Author(s) -
Yang ShawYang,
Yeh HundDer
Publication year - 2007
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2007wr006431
Subject(s) - function (biology) , decimal , mathematics , table (database) , binomial coefficient , limit (mathematics) , computation , algorithm , discrete mathematics , computer science , arithmetic , mathematical analysis , evolutionary biology , biology , data mining
where x = y/a. Equations (2)–(4) are evaluated by directly adding the infinite series; yet, the numerical evaluation is not straightforward and the accuracy of the results are not easy to evaluate because of the fact that the series involves the incomplete Gamma function and has a running sum from zero to infinity. [2] In this comment, we provide a simple and efficient numerical approach as an alternative to evaluate the Hantush’s M function. The Gaussian quadrature is employed to perform the numerical integration of equation (1) piecewise along the y axis from (0, a) to ( 1, 1) where a change of variable has been used. An n-point Gaussian quadrature formula may be written as [Gerald and Wheatley, 1989] Z 1