In the analytic theory of continued fractions, Euler's continued fraction formula is an identity connecting a certain very general infinite series with an infinite continued fraction. First published in 1748, it was at first regarded as a simple identity connecting a finite sum with a finite continued fraction in such a way that the extension to the infinite case was immediately apparent. Today it is more fully appreciated as a useful tool in analytic attacks on the general convergence problem for infinite continued fractions with complex elements.
Read more about Euler's Continued Fraction Formula: The Original Formula, Euler's Formula in Modern Notation
Famous quotes containing the words continued, fraction and/or formula:
“The protection of a ten-year-old girl from her father’s advances is a necessary condition of social order, but the protection of the father from temptation is a necessary condition of his continued social adjustment. The protections that are built up in the child against desire for the parent become the essential counterpart to the attitudes in the parent that protect the child.”
—Margaret Mead (1901–1978)
“The mother as a social servant instead of a home servant will not lack in true mother duty.... From her work, loved and honored though it is, she will return to her home life, the child life, with an eager, ceaseless pleasure, cleansed of all the fret and fraction and weariness that so mar it now.”
—Charlotte Perkins Gilman (1860–1935)
“My formula for greatness in human beings is amor fati: that one wants to change nothing, neither forwards, nor backwards, nor in all eternity. Not merely to endure necessity, still less to hide it—all idealism is mendacity in the face of necessity—but rather to love it.”
—Friedrich Nietzsche (1844–1900)