What windowed Sinc might be closest to a Parks–McClellan low-pass filter? In another question on dsp.stackexchange, a statement was made that the output of MATLAB firpm() or firls() for an anti-alias low-pass filter was "close" to the coefficients of a windowed-Sinc low-pass filter.  

If so:

What window (applied to a Sinc "perfect" reconstruction waveform) would provide low-filter kernel coefficients closest (In least squared error or other commonly used metric) to those of a same-length FIR filter designed by the Parks–McClellan or Remez-exchange methods?  Is it one of the well-known named window functions (Nuttall et.al.)?  Or is there a good numerical or tractable equation approximation to this window?
none.

what you're asking for is what window, which multiplies a sinc() function, will get you an optimal impulse response kernel, like you might get from Parks-McClellan.  well, to get that window, you must undo the multiplication.

the problem is that you cannot divide by zero.  any of these "sinc-like" functions that come out of P-McC will pass through 0.  but not necessarily at the same place that the sinc() function goes through zero.