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From: lew@ihuxr.UUCP
Newsgroups: net.math
Subject: Identity reference found
Message-ID: <550@ihuxr.UUCP>
Date: Thu, 11-Aug-83 18:31:04 EDT
Article-I.D.: ihuxr.550
Posted: Thu Aug 11 18:31:04 1983
Date-Received: Sat, 13-Aug-83 02:56:11 EDT
Organization: BTL Naperville, Il.
Lines: 20

John Riordan gives my "interesting identity" as an example on page 4
of his appropriately titled book, "Combinatorial Identities". He gives
the inductive proof but he skips most of the algebra. He takes things
one step further. Having defined the inverse relations:

	a(n) = sum k=0,n of (-1)^k * C(n,k) * b(k)

	b(n) = sum k=0,n of (-1)^k * C(n,k) * a(k)

... he lets b(0)=0, b(k) = 1/k. This gives for a(n) the negative of the
expression we just showed equal to 1 + 1/2 + ... + 1/n. The second
relation then relates 1/n to a sum over sums of 1/k. He shows this
directly then states,

"The first derivation is somewhat simpler, thus providing a point to the
Jacobian injunction 'always invert'."

A point? ... oh well, he's only up to page 5!

	Lew Mammel, Jr. ihuxr!lew