Re: Wolfram, meet Stefan and Boltzmann
- To: mathgroup at smc.vnet.net
- Subject: [mg117389] Re: Wolfram, meet Stefan and Boltzmann
- From: AES <siegman at stanford.edu>
- Date: Thu, 17 Mar 2011 06:30:40 -0500 (EST)
- References: <email@example.com>
David Lichtbau notes: > (3) Find the antiderivative. It is > > In:= InputForm[Integrate[x^3/(Exp[x] - 1), x]] > > Out//InputForm= > -x^4/4 + x^3*Log[1 - E^x] + 3*x^2*PolyLog[2, E^x] - > 6*x*PolyLog[3, E^x] + 6*PolyLog[4, E^x] The original integral shown above is used to evaluate the Stefan-Boltzmann constant sigma in the expression P/A = sigma T^4 for total power per unit area radiated by a blackbody surface at temperature T. Physically it represents integrating over all the frequencies or wavelengths coming from the blackbody radiator. I'm not personally familiar with the term "antiderivative" (nor the term "PolyLog" for that matter); but if it means in essence "indefinite integral" then this antiderivative might be used to evaluate the total P/A coming from a _frequency_ or _spectrally_ filtered blackbody source using a flat-topped passband filter. Hmm -- wonder if the thermodynamic or blackbody-radiation communities know about that?