In article <4E35AB1E.email@example.com>, "Stephen J. Herschkorn" <firstname.lastname@example.org> wrote: >G.Waleed Kavalec wrote: > >>Question: Is there a continuous function that maps to the harmonic >>series at the integers? >> >>Given that for x at integer n, y = sum (1 ... 1/n). >> >>Is there a smooth continuous f(x) that is equivalent? >> >> >"H_n = g + f(n+1), where g is the Euler-Mascheoni constant and f is >the digama function.." > >http://mathworld.wolfram.com/HarmonicNumber.html (which uses themore >usual Greek charactters in place of "g" and "f")
This function can also be obtained as
+oo --- 1 1 H(n) = > ( - - --- ) --- k k+n k=1
which converges absolutely for all complex n.
Rob Johnson <email@example.com> take out the trash before replying to view any ASCII art, display article in a monospaced font