Wikipedia:Reference desk/Archives/Mathematics/2015 July 26
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July 26
editDifferential equation
editWhat are the solutions of ? Examples include f arbitrary and g(x) = x, and f(x) = x2 and g = sin. GeoffreyT2000 (talk) 01:33, 26 July 2015 (UTC)
an obscure root-finding problem
editI expect the answer is No, but anyway: if , is there a closed expression for r given x,y? —Tamfang (talk) 08:40, 26 July 2015 (UTC)
- There is! But it requires use of the non-elementary Lambert W function: . -- Meni Rosenfeld (talk) 09:15, 26 July 2015 (UTC)
- Thanks! Looks like I need to install SciPy. —Tamfang (talk) 19:56, 26 July 2015 (UTC)
- ...or work out the Taylor series (with y as the variable, in my application). —Tamfang (talk) 21:03, 27 July 2015 (UTC)
A closed expression is not necessarily useful. Set s = r–1. Then the equation is 0 = exs–ys. Expand the exponential: . Leave it here until you need numeric solutions. Bo Jacoby (talk) 22:30, 26 July 2015 (UTC).
- Numeric solutions are, as it happens, all I need. —Tamfang (talk) 21:03, 27 July 2015 (UTC)
- If that. It hit me last night that the idea for which I asked this question was backward. Is that a valid reason to mark it Resolved? —Tamfang (talk) 06:14, 29 July 2015 (UTC)
Let and . A root s in the algebraic equation approximately solves the transcendental equation when N is not too small. If you supply values for x and y I'll show you how to solve it. Bo Jacoby (talk) 06:54, 28 July 2015 (UTC).