Products of Series
The Cauchy product of two series converges to the product of the sums if at least one of the series converges absolutely. That is, suppose that
- and .
The Cauchy product is defined as the sum of terms cn where:
Then, if either the an or bn sum converges absolutely, then
Read more about this topic: Absolute Convergence
Famous quotes containing the words products of, products and/or series:
“We are the products of editing, rather than of authorship.”
—George Wald (b. 1906)
“The reality is that zero defects in products plus zero pollution plus zero risk on the job is equivalent to maximum growth of government plus zero economic growth plus runaway inflation.”
—Dixie Lee Ray (b. 1924)
“A sophistical rhetorician, inebriated with the exuberance of his own verbosity, and gifted with an egotistical imagination that can at all times command an interminable and inconsistent series of arguments to malign an opponent and to glorify himself.”
—Benjamin Disraeli (1804–1881)