Re: [math-fun] harmonic series, Gosper 1974

Specifically Gosper 1974 found H(x) = -SUM(j=1,2,3...) (1/j) * (j+x)^(-1) * (3*j+x) * binomial(j-x-1, j) / binomial(2j, j) where H(n) = 1 + 1/2 + 1/3 + ... + 1/n. Each summand in Gosper's series is a rational function of x with denominator=j+x and having numerator which is a polynomial(x) of degree=j+1. With a little cleverness, the first N terms in Gosper's series can all be computed in O(N) arithmetic operations. My question was, what if anything is the corresponding formula for 1 + 1/3 + 1/5 + ... + 1/(2*n-1). -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)