This is indeed a loss. And a lost opportunity for perhaps a nice little tiff over his last paper (with J. Borwein) “Closed forms: What they are and why we care,” http://www.ams.org/notices/201301/rnoti-p50.pdf p63: Relatedly, the classical Bessel expansion is BesselK[0, z] == Sum[((z/2)^n/n!)^2*Sum[1/k, {k, n - 1}], {n, ∞}] - (Log[z/2] + EulerGamma)*BesselI[0, z] Now K0(z) has a (degenerate) Meijer-G representation—so potentially is superclosed for algebraic z—and I0(z) is accordingly hyperclosed, but the nested harmonic series on the right is again problematic. I have three problems with these two sentences! First, the equation should be BesselK[0, z] == Sum[((z/2)^n/n!)^2*Sum[1/k, {k, n}], {n, ∞}] - (Log[z/2] + EulerGamma)*BesselI[0, z] Next, the nested harmonic series is NOT problematic. You can compute it linearly as the 3by3 product of MProd[{{z^2/(4*k^2), z^2/(4*k^3), 0}, {0, z^2/(4*k^2), 1}, {0, 0, 1}}, {k, Infinity}] It would be a mistake to exclude such products from "hyperclosed" (i.e., simple functions of hypergeometric values.) Lastly, the γ arises because K₀ has confluent poles as a Meijer-G. This "degeneracy" makes it unhypergeometric. Now, we have only Jon to blame. --rwg On 2012-12-22, at 9:59 AM, rcs@xmission.com wrote: Bob Baillie passed along this note from the experimental math blog of David Bailey and Jonathan Borwein. --Rich Forwarded message from rjbaillie@frii.com Subject: Mathematician/physicist/inventor Richard Crandall dies at 64 http://experimentalmath.info/blog/2012/12/mathematicianphysicistinventor-ric...