Science Forums 2

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Actually Don's case is of one variable so neither Gauss-Seidel nor Newton-Raphson are necessary. I think the best bet is to use Newton's method; the derivative isn't all that wicked; unless I've made one of my terrible blunders it's:





Now to reach 60 decimal places, starting from the value already estimated, prolly takes quite a lot of iterations and, since consecutive values will certainly be within the convergence basin, it might be worthwile using an alteration of Newton's method which I have tried in the past but I'm not sure which would be computationally less intensive. It depends on the weight of one extra ln and subtraction against an extra multiplication and three extra divisions; if the natural logarithm is lightweight enough in perl the trick could be faster.