Re: Rademacher formula for p(n) with PARI

[harley@argote.ch (Dr. Robert Harley)]

Another remark:

The following formula (which appears to be more efficient) for the
first factor of the terms appears (essentially) in Lehmer's paper:

  partfac1(q, n) = local(rb); sum(r = 0, q-1, if(gcd(r, q)>1, 0, rb = lift(1/Mod(r, q)); cos(if(q%2, -24*n*r-6*q*kronecker(-r, q)-3*q*(q-3)-(sqr(q)-1)*(2*r+rb-sqr(r)*rb), -24*n*r-6*q*kronecker(-q, r)+r*(q+1)*(q+2)+(sqr(q)-1)*(sqr(r)-1)*rb)*Pi/12/q)))

There are also some interesting multiplication theorems to reduce to
the case where q is a prime power... surely these would be useful for
implementation. :-/

Bye,
  Rob.
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