difficulty using FindRoot
- To: mathgroup at smc.vnet.net
- Subject: [mg110231] difficulty using FindRoot
- From: Roger Bagula <roger.bagula at gmail.com>
- Date: Wed, 9 Jun 2010 07:21:29 -0400 (EDT)
The question of a q-form infinite exponential series solving to give Pi came up. I had absolutely no luck with infinite sums on this! I tried a plot of the function to narrow it down: Clear[f, x, n, i] f[x_] := 1 + Sum[1/Product[1 - x^i, {i, 1, n}], {n, 1, 100}] Plot[f[x], {x, 1.021831198825114750405873564886860549451, 1.02183648425181683450091441045515239239}, PlotRange -> All] The find root that seemed to work was: q /. FindRoot[1 + Sum[1/Product[1 - q^i, {i, 1, n}], {n, 1, 150}] - Pi == 0, {q, 1.0218701842518167}, WorkingPrecision -> 800, AccuracyGoal -> 795] gives: 1.0218311988251147504058736 with error messages: \!\(Divide::"infy" \(\(:\)\(\ \)\) "Infinite expression \!\(3.14159265346825122833252`25.0094071873645\/0\) \ encountered."\) \!\(\* RowBox[{\(FindRoot::"jsing"\), \(\(:\)\(\ \)\), "\<\"Encountered a singular Jacobian at the point \\!\\({q}\\) = \ \\!\\({1.0218311988251147504058736`25.0094071873645}\\). Try perturbing the \ initial point(s). \\!\\(\\*ButtonBox[\\\"More=85\\\", \ ButtonStyle->\\\"RefGuideLinkText\\\", ButtonFrame->None, \ ButtonData:>\\\"FindRoot::jsing\\\"]\\)\"\>"}]\) 1 + Sum[1/Product[1 - (1.02183119882511475040587356488686054945)^i, {i, 1, n}], {n, 1, 150}] gives 0*10^(-19) It appears there is no real q such that the sum? 1 + Sum[1/Product[1 - q^i, {i, 1, n}], {n, 1, Infinity}]==Pi Respectfully, Roger L. Bagula 11759 Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 : http://www.google.com/profiles/Roger.Bagula alternative email: roger.bagula at gmail.com
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- From: Daniel Lichtblau <danl@wolfram.com>
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