Robert wrote: << For the poor, unfortunate souls who have no idea why Gosper said "shew that": http://i.imgur.com/lmFFL.jpg
It that by any chance Whattaker & Witson? I remember that the summer after high school I was excited by the idea of finding a natural continuous function f(x) whose value at each positive integers n was f(n) = H_n := 1 + 1/2 + . . . + 1/n. This wasn't too hard, integrating from 0 to 1 the formula 1+u+...+u^(n-1) = (1-u^n)/(1-u) and allowing the n on the RHS to take real values. Soon I generalized it to sums of real powers of the reciprocals of integers. What felt like a really neat conclusion was that, letting the n -> oo, this led to an integral formula for Gamma(x)*Zeta(x). (Of course I had no idea at age 17 of how to make such a proof rigorous, and didn't yet know about contour integrals in C.) Still, all excited about this formula, I told it to my freshman advisor, Henry McKean, on the first day we met. He casually reached over to his bookshelf, and after flipping a few pages showed me the identical formula in Whittaker an Watson from 70 years earlier. You've never seen an MIT freshman's bubble burst so quickly. --Dan ________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx