*attempts to put this thread back on track*
I spent several hours last night trying to derive a series representation for this:
¥
òx-xdx
0
This converges to a constant value surprisingly close to 2, around 1.995455977898199. I have been able to obtain a series for the indefinite HXI function of order 2,
¥ k
å å [ xk+1 (k+1)n k! logk(-x) ] / [ (-1)k+n (k+1)k+1 n! ]
k=0 n=0
but cannot easily find the limit of this thing as x tends to infinity since this is a double generalized power series and reducing it to a single sum introduces incomplete gamma functions. (which are also hard to work with in limits) Its convergence is fairly slow so it is numerically pretty useless, and I would like an exact symbolic representation anyway. Anyone know how to take the limit of this?